Geldof, who comes from Dublin, appeared in a video for the Irish4Europe campaign urging Irish nationals in Britain to register to vote by the June 7 deadline.
The campaign says it is targeting around 600,000 Irish-born people living and working in Britain.
Irish citizens aged 18 or over and resident in the Britain or Gibraltar can vote in the referendum, as can Commonwealth citizens.
In the video, Geldof, 64, lists people he will be encouraging to vote "Remain" in the June 23 referendum on Britain's EU membership.
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"Whether there would be border controls or custom controls, these things are a possibility but obviously they would require some very serious negotiations," he said of the prospect of Brexit, or Britain exiting the EU.
Ireland and Britain entered the European Economic Community at the same time in 1973 and share a passport-free Common Travel Area.
"Ireland's position on the EU-UK question is clear: We want the UK, as our friend, closest neighbour and partner, to remain a member of a reformed EU," the Irish embassy says on its website.