diff --git a/.changeset/rare-rice-throw.md b/.changeset/rare-rice-throw.md
new file mode 100644
index 0000000000..6fa0434f67
--- /dev/null
+++ b/.changeset/rare-rice-throw.md
@@ -0,0 +1,5 @@
+---
+'@backstage/core-components': patch
+---
+
+Add `tooltipClasses` prop to `OverflowTooltip` component to allow customisation of the tooltip
diff --git a/packages/core-components/src/components/OverflowTooltip/OverflowTooltip.tsx b/packages/core-components/src/components/OverflowTooltip/OverflowTooltip.tsx
index 68499e2dc1..7fc45d767d 100644
--- a/packages/core-components/src/components/OverflowTooltip/OverflowTooltip.tsx
+++ b/packages/core-components/src/components/OverflowTooltip/OverflowTooltip.tsx
@@ -23,6 +23,7 @@ type Props = {
   title?: TooltipProps['title'];
   line?: number | undefined;
   placement?: TooltipProps['placement'];
+  tooltipClasses?: TooltipProps['classes'];
 };
 
 export type OverflowTooltipClassKey = 'container';
@@ -51,6 +52,7 @@ export function OverflowTooltip(props: Props) {
     <Tooltip
       title={props.title ?? (props.text || '')}
       placement={props.placement}
+      classes={props.tooltipClasses}
     >
       <Typography className={classes.typo} variant="inherit">
         {props.text}