diff --git a/packages/grafana-ui/src/components/VizTooltip/VizTooltip.tsx b/packages/grafana-ui/src/components/VizTooltip/VizTooltip.tsx
index 816038b817e..c5324bfa8aa 100644
--- a/packages/grafana-ui/src/components/VizTooltip/VizTooltip.tsx
+++ b/packages/grafana-ui/src/components/VizTooltip/VizTooltip.tsx
@@ -1,7 +1,10 @@
 import React from 'react';
+import { css } from '@emotion/css';
+import { Portal } from '../Portal/Portal';
 import { Dimensions, TimeZone } from '@grafana/data';
 import { FlotPosition } from '../Graph/types';
 import { VizTooltipContainer } from './VizTooltipContainer';
+import { useStyles } from '../../themes';
 import { TooltipDisplayMode } from './models.gen';
 
 // Describes active dimensions user interacts with
@@ -46,14 +49,30 @@ export interface VizTooltipProps {
  * @public
  */
 export const VizTooltip: React.FC<VizTooltipProps> = ({ content, position, offset }) => {
+  const styles = useStyles(getStyles);
   if (position) {
     return (
-      <VizTooltipContainer position={position} offset={offset || { x: 0, y: 0 }}>
-        {content}
-      </VizTooltipContainer>
+      <Portal className={styles.portal}>
+        <VizTooltipContainer position={position} offset={offset || { x: 0, y: 0 }}>
+          {content}
+        </VizTooltipContainer>
+      </Portal>
     );
   }
   return null;
 };
 
 VizTooltip.displayName = 'VizTooltip';
+
+const getStyles = () => {
+  return {
+    portal: css`
+      position: absolute;
+      top: 0;
+      left: 0;
+      pointer-events: none;
+      width: 100%;
+      height: 100%;
+    `,
+  };
+};
diff --git a/packages/grafana-ui/src/components/VizTooltip/VizTooltipContainer.tsx b/packages/grafana-ui/src/components/VizTooltip/VizTooltipContainer.tsx
index 137045fc706..a27464f0c86 100644
--- a/packages/grafana-ui/src/components/VizTooltip/VizTooltipContainer.tsx
+++ b/packages/grafana-ui/src/components/VizTooltip/VizTooltipContainer.tsx
@@ -1,9 +1,10 @@
-import React, { useState, HTMLAttributes, useMemo } from 'react';
+import React, { useState, HTMLAttributes, useMemo, useRef, useLayoutEffect } from 'react';
 import { css, cx } from '@emotion/css';
 import { useStyles2 } from '../../themes';
 import { getTooltipContainerStyles } from '../../themes/mixins';
-import { GrafanaTheme2 } from '@grafana/data';
-import { usePopper } from 'react-popper';
+import useWindowSize from 'react-use/lib/useWindowSize';
+import { Dimensions2D, GrafanaTheme2 } from '@grafana/data';
+import { calculateTooltipPosition } from './utils';
 
 /**
  * @public
@@ -24,47 +25,76 @@ export const VizTooltipContainer: React.FC<VizTooltipContainerProps> = ({
   className,
   ...otherProps
 }) => {
-  const [tooltipRef, setTooltipRef] = useState<HTMLDivElement | null>(null);
-  const virtualElement = useMemo(
-    () => ({
-      getBoundingClientRect() {
-        return { top: positionY, left: positionX, bottom: positionY, right: positionX, width: 0, height: 0 };
-      },
-    }),
-    [positionY, positionX]
-  );
-  const { styles: popperStyles, attributes } = usePopper(virtualElement, tooltipRef, {
-    placement: 'bottom-start',
-    modifiers: [
-      { name: 'arrow', enabled: false },
-      {
-        name: 'preventOverflow',
-        enabled: true,
-        options: {
-          altAxis: true,
-          rootBoundary: 'viewport',
-        },
-      },
-      {
-        name: 'offset',
-        options: {
-          offset: [offsetX, offsetY],
-        },
-      },
-    ],
+  const tooltipRef = useRef<HTMLDivElement>(null);
+  const [tooltipMeasurement, setTooltipMeasurement] = useState<Dimensions2D>({ width: 0, height: 0 });
+  const { width, height } = useWindowSize();
+  const [placement, setPlacement] = useState({
+    x: positionX + offsetX,
+    y: positionY + offsetY,
   });
 
+  const resizeObserver = useMemo(
+    () =>
+      // TS has hard time playing games with @types/resize-observer-browser, hence the ignore
+      // @ts-ignore
+      new ResizeObserver((entries) => {
+        for (let entry of entries) {
+          const tW = Math.floor(entry.contentRect.width + 2 * 8); //  adding padding until Safari supports borderBoxSize
+          const tH = Math.floor(entry.contentRect.height + 2 * 8);
+          if (tooltipMeasurement.width !== tW || tooltipMeasurement.height !== tH) {
+            setTooltipMeasurement({
+              width: tW,
+              height: tH,
+            });
+          }
+        }
+      }),
+    [tooltipMeasurement]
+  );
+
+  useLayoutEffect(() => {
+    if (tooltipRef.current) {
+      resizeObserver.observe(tooltipRef.current);
+    }
+
+    return () => {
+      resizeObserver.disconnect();
+    };
+  }, [resizeObserver]);
+
+  // Make sure tooltip does not overflow window
+  useLayoutEffect(() => {
+    if (tooltipRef && tooltipRef.current) {
+      const { x, y } = calculateTooltipPosition(
+        positionX,
+        positionY,
+        tooltipMeasurement.width,
+        tooltipMeasurement.height,
+        offsetX,
+        offsetY,
+        width,
+        height
+      );
+
+      setPlacement({ x, y });
+    }
+  }, [width, height, positionX, offsetX, positionY, offsetY, tooltipMeasurement]);
+
   const styles = useStyles2(getStyles);
 
   return (
     <div
-      ref={setTooltipRef}
+      ref={tooltipRef}
       style={{
-        ...popperStyles.popper,
-        display: popperStyles.popper?.transform ? 'block' : 'none',
-        transition: 'all ease-out 0.2s',
+        position: 'fixed',
+        left: 0,
+        // disabling pointer-events is to prevent the tooltip from flickering when moving left to right
+        // see e.g. https://github.com/grafana/grafana/pull/33609
+        pointerEvents: 'none',
+        top: 0,
+        transform: `translate(${placement.x}px, ${placement.y}px)`,
+        transition: 'transform ease-out 0.1s',
       }}
-      {...attributes.popper}
       {...otherProps}
       className={cx(styles.wrapper, className)}
     >
diff --git a/packages/grafana-ui/src/components/VizTooltip/utils.test.ts b/packages/grafana-ui/src/components/VizTooltip/utils.test.ts
new file mode 100644
index 00000000000..92c59cdba5c
--- /dev/null
+++ b/packages/grafana-ui/src/components/VizTooltip/utils.test.ts
@@ -0,0 +1,165 @@
+import { calculateTooltipPosition } from './utils';
+
+describe('utils', () => {
+  describe('calculateTooltipPosition', () => {
+    // let's pick some easy numbers for these, we shouldn't need to change them
+    const tooltipWidth = 100;
+    const tooltipHeight = 100;
+    const xOffset = 10;
+    const yOffset = 10;
+    const windowWidth = 200;
+    const windowHeight = 200;
+
+    it('sticky positions the tooltip to the right if it would overflow at both ends but overflow to the left more', () => {
+      const xPos = 99;
+      const yPos = 50;
+      const result = calculateTooltipPosition(
+        xPos,
+        yPos,
+        tooltipWidth,
+        tooltipHeight,
+        xOffset,
+        yOffset,
+        windowWidth,
+        windowHeight
+      );
+      expect(result).toEqual({
+        x: 90,
+        y: 60,
+      });
+    });
+
+    it('sticky positions the tooltip to the left if it would overflow at both ends but overflow to the right more', () => {
+      const xPos = 101;
+      const yPos = 50;
+      const result = calculateTooltipPosition(
+        xPos,
+        yPos,
+        tooltipWidth,
+        tooltipHeight,
+        xOffset,
+        yOffset,
+        windowWidth,
+        windowHeight
+      );
+      expect(result).toEqual({
+        x: 10,
+        y: 60,
+      });
+    });
+
+    it('positions the tooltip to left of the cursor if it would overflow right', () => {
+      const xPos = 150;
+      const yPos = 50;
+      const result = calculateTooltipPosition(
+        xPos,
+        yPos,
+        tooltipWidth,
+        tooltipHeight,
+        xOffset,
+        yOffset,
+        windowWidth,
+        windowHeight
+      );
+      expect(result).toEqual({
+        x: 40,
+        y: 60,
+      });
+    });
+
+    it('positions the tooltip to the right of the cursor if it would not overflow', () => {
+      const xPos = 50;
+      const yPos = 50;
+      const result = calculateTooltipPosition(
+        xPos,
+        yPos,
+        tooltipWidth,
+        tooltipHeight,
+        xOffset,
+        yOffset,
+        windowWidth,
+        windowHeight
+      );
+      expect(result).toEqual({
+        x: 60,
+        y: 60,
+      });
+    });
+
+    it('sticky positions the tooltip to the bottom if it would overflow at both ends but overflow to the top more', () => {
+      const xPos = 50;
+      const yPos = 99;
+      const result = calculateTooltipPosition(
+        xPos,
+        yPos,
+        tooltipWidth,
+        tooltipHeight,
+        xOffset,
+        yOffset,
+        windowWidth,
+        windowHeight
+      );
+      expect(result).toEqual({
+        x: 60,
+        y: 90,
+      });
+    });
+
+    it('sticky positions the tooltip to the top if it would overflow at both ends but overflow to the bottom more', () => {
+      const xPos = 50;
+      const yPos = 101;
+      const result = calculateTooltipPosition(
+        xPos,
+        yPos,
+        tooltipWidth,
+        tooltipHeight,
+        xOffset,
+        yOffset,
+        windowWidth,
+        windowHeight
+      );
+      expect(result).toEqual({
+        x: 60,
+        y: 10,
+      });
+    });
+
+    it('positions the tooltip above the cursor if it would overflow at the bottom', () => {
+      const xPos = 50;
+      const yPos = 150;
+      const result = calculateTooltipPosition(
+        xPos,
+        yPos,
+        tooltipWidth,
+        tooltipHeight,
+        xOffset,
+        yOffset,
+        windowWidth,
+        windowHeight
+      );
+      expect(result).toEqual({
+        x: 60,
+        y: 40,
+      });
+    });
+
+    it('positions the tooltip below the cursor if it would not overflow', () => {
+      const xPos = 50;
+      const yPos = 50;
+      const result = calculateTooltipPosition(
+        xPos,
+        yPos,
+        tooltipWidth,
+        tooltipHeight,
+        xOffset,
+        yOffset,
+        windowWidth,
+        windowHeight
+      );
+      expect(result).toEqual({
+        x: 60,
+        y: 60,
+      });
+    });
+  });
+});
diff --git a/packages/grafana-ui/src/components/VizTooltip/utils.ts b/packages/grafana-ui/src/components/VizTooltip/utils.ts
new file mode 100644
index 00000000000..6517962fc07
--- /dev/null
+++ b/packages/grafana-ui/src/components/VizTooltip/utils.ts
@@ -0,0 +1,40 @@
+export const calculateTooltipPosition = (
+  xPos = 0,
+  yPos = 0,
+  tooltipWidth = 0,
+  tooltipHeight = 0,
+  xOffset = 0,
+  yOffset = 0,
+  windowWidth = 0,
+  windowHeight = 0
+) => {
+  let x = xPos;
+  let y = yPos;
+
+  const overflowRight = Math.max(xPos + xOffset + tooltipWidth - (windowWidth - xOffset), 0);
+  const overflowLeft = Math.abs(Math.min(xPos - xOffset - tooltipWidth - xOffset, 0));
+  const wouldOverflowRight = overflowRight > 0;
+  const wouldOverflowLeft = overflowLeft > 0;
+
+  const overflowBelow = Math.max(yPos + yOffset + tooltipHeight - (windowHeight - yOffset), 0);
+  const overflowAbove = Math.abs(Math.min(yPos - yOffset - tooltipHeight - yOffset, 0));
+  const wouldOverflowBelow = overflowBelow > 0;
+  const wouldOverflowAbove = overflowAbove > 0;
+
+  if (wouldOverflowRight && wouldOverflowLeft) {
+    x = overflowRight > overflowLeft ? xOffset : windowWidth - xOffset - tooltipWidth;
+  } else if (wouldOverflowRight) {
+    x = xPos - xOffset - tooltipWidth;
+  } else {
+    x = xPos + xOffset;
+  }
+
+  if (wouldOverflowBelow && wouldOverflowAbove) {
+    y = overflowBelow > overflowAbove ? yOffset : windowHeight - yOffset - tooltipHeight;
+  } else if (wouldOverflowBelow) {
+    y = yPos - yOffset - tooltipHeight;
+  } else {
+    y = yPos + yOffset;
+  }
+  return { x, y };
+};