Announcing his candidacy in a newspaper article, he promised to bring "fresh new ideas" to the debate and said he was representing a "new and talented generation" of Tory MPs.
Mr Malthouse is best known for his role in bringing together Leave and Remain Tory MPs to draw up the so-called "Malthouse Compromise" in a bid to secure the House of Commons' support for Ms May's Brexit deal.
The proposal would have seen the deal approved if the controversial Northern Ireland backstop element was replaced by "alternative arrangements".
The North West Hampshire MP said there was a "yearning for change" among voters.
Writing in The Sun, he said: "This leadership campaign cannot be about the same old faces, scarred by wars that have split the Tory party over three years.
"I believe I’m the new face, with fresh new ideas, from a new and talented generation."
He added: "We need to end the Brexit paralysis, and while I voted to leave the EU, I know that without unity across the UK, we cannot get a deal over the line.
"It's time for a new generation to lead the charge into our future with boldness and vision."
Mr Malthouse is a former deputy mayor of London and entered the Commons in 2015.
He is the tenth candidate to join the contest to be the next prime minister, announcing his campaign shortly after Sajid Javid, the home secretary, confirmed his own bid to replace Ms May.
As the race stepped up a gear, several candidates unveiled their first policies.
Michael Gove, the environment secretary, said he would offer free British citizenship to three million EU nationals living in the UK, while health secretary Matt Hancock said his plan would involve "driving up the Living Wage and cutting taxes".
Rory Stewart, the international development secretary, received a boost when he was endorsed by Tory grandee Sir Nicholas Soames, the grandson of Sir Winston Churchill.
Writing in the Daily Mail, Sir Nicholas said there was only one candidate "who can sort out Brexit, unite our party and restore pride and hope to Britain".
He said: "That person is Rory Stewart. I am honoured to support him.
"Some say we can leave the EU without a deal. But this would be the greatest insult to the wisdom and understanding of the British people.
"They don't want a leader who offers to ruin our country. They want one to lead it.
"Easy lies and false simplicities got us into this mess. They will emphatically not get us out of it."
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