He has said he will not invoke Article 50 and will leave the exit timetable to his successor.
He wants to see a new Conservative leader in place by the party conference in October.
Boris Johnson, who has been given much of the credit for winning the referendum, is favourite to succeed Mr Cameron.
However, Mr Gove and prominent Brexiteer Andrea Leadsom are also among the favourites.
It is thought major policy decisions, including Heathrow airport expansion and the renewal of Trident, will now be delayed until after the new leader is elected.