Gove lost the Conservative Party's final ballot of members of Parliament by two votes to Hunt, who received 77. Johnson solidified his front-runner status with 160 votes.
"Naturally disappointed but so proud of the campaign we ran," Gove tweeted after the vote. "Huge thanks to my brilliant campaign team. It's been an honour to be able to set out a vision for the future of our great country. Many congratulations to Boris and Jeremy!"
Johnson and Hunt will now face each other in a vote of some 160,000 party members through a postal ballot. The winner will be announced the fourth week in July.
An earlier round of voting Thursday knocked out Sajid Javid, who finished last with 34 votes.
Johnson, one of the leading voices of support for Britain leaving the European Union, led the race comfortably in previous voting and is the lead candidate to replace May as prime minister. He has promised to leave the EU with or without a deal on Oct. 31. May is resigning after failing to sell lawmakers on an exit agreement.
Irish Prime Minister Leon Varadkar said whoever succeeds May will have to work with the same proposal May struggled with. As it's highly unlikely the EU will agree to any more negotiations, the next leader will basically have to decide whether to leave the alliance without an agreement.
Gove and Hunt have said they're open to delaying the exit again, if it means securing a new deal. Johnson has said there will be no more delays.