ITV reported this afternoon that Gove will chair the campaigning committee, while Labour MP Gisela Stuart is set to chair the campaign group's formal board, replacing former chancellor Lord Lawson.
Vote Leave is one of multiple eurosceptic groups vying for official campaign status in the run-up to the referendum on Britain's European Union membership on 23 June. Grassroots Out (GO) and Leave.EU have also made clear that they want the Electoral Commission's seal of approval.
Gove, a close ally of Prime Minister David Cameron, revealed last month that he would be campaigning for the UK to leave the EU.
The justice secretary has come under fire today amid accusations that he leaked details to the Sun newspaper that Queen Elizabeth II is eurosceptic.
Gove was reportedly present at a lunch at Windsor Castle involving former deputy prime minister Nick Clegg and the Queen. The Sun reported that the Queen told Clegg she thought Europe was going in the wrong direction.
Buckingham Palace has rejected the reports, saying the Queen is "politically neutral".
The Palace has also complained to the press watchdog IPSO that the Sun's story was misleading.