He said he had taken the drug at social gatherings when he was a young journalist.
"It was a mistake. I look back and I think I wish I hadn't done that," he said. "It was 20 years ago and yes, it was a mistake. But I don't believe that past mistakes disqualify you."
Gove said he hoped that the disclosure would not prevent him being appointed the next prime minister.
"Obviously it will be for my colleagues in parliament and members of the Conservative Party to decide now if I should be leader," he said. "I think all politicians have lives before politics."
Gove made his admission ahead of publication of a book about him by political journalist Owen Bennett.
The book – Michael Gove: A Man in a Hurry – says the environment secretary owned up to having used cocaine when he was being ‘put through his paces’ by advisers in the 2016 Tory leadership contest.
The startling admission came when he and the aides were trying to anticipate what questions he would face from the media.
An inside source said Gove said ‘Yes, cocaine’ when asked if he had ever taken drugs.
The revelation comes as the contest to replace May is gathering pace with candidates arguing over the rights and wrongs of a so-called no-deal Brexit, or leaving the EU without a deal.
May stepped down as leader of the governing Conservatives on Friday, officially triggering a contest to replace her that could see her party embrace a tougher stance on Brexit.
Candidates must announce whether they are standing in the contest by Monday. The selection process should be completed by the end of July.