The MP for North West Hampshire, widely credited as the convener of both Conservative Leavers and Remainers to develop a compromise on Mrs May’s withdrawal agreement, said there was a “yearning for change”.
He launched his bid with an article in The Sun, adding that it was “time for a new generation to lead the charge into our future”.
The 52-year-old is a former deputy mayor of London and entered the Commons in 2015 as David Cameron’s Conservatives won a majority.
His name was given to the so-called Malthouse Compromise – a proposal drawn up by backbenchers from Leave and Remain wings of the Tory Party, which would have implemented Mrs May’s Brexit deal with the backstop replaced by alternative arrangements.
He wrote: “This leadership campaign cannot be about the same old faces, scarred by wars that have split the Tory party over three years.
“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.”
As the race to succeed Mrs May enters its first full week, each candidate has started offering a flavour for what their policies would be.
Michael Gove is prepared to offer free UK citizenship to three million nationals who resided in the UK at the time of the June 2016 referendum, while Matt Hancock wrote in the Daily Mail about “driving up the Living Wage and cutting taxes”.
The Health Secretary wrote: “Instead of yet another battle over Brexit, the next election should be about the economy – the territory on which the Conservative Party wins.
“It should be a clear choice between higher pay with the Tories or higher taxes with Corbyn’s Labour.”
Mid Sussex MP Rory Stewart’s campaign was endorsed by Sir Nicholas Soames, grandson of former Prime Minister Sir Winston Churchill.
The 36-year veteran of the Commons wrote in the Daily Mail there was only one person who had put their name forward “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.”
Former Cabinet ministers Andrea Leadsom, Esther McVey, Dominic Raab and Boris Johnson have also announced they would like to replace Mrs May.
William Hague, who led the Conservative party in opposition between 1997 and 2001, urged candidates to “recognise the absence of certainty and go for honesty”.
Writing in the Daily Telegraph, he said: “If they are not careful, they are going to be swept up in the tidal wave of a rampaging Brexit Party and dashed against the sharp rocks of a hostile House of Commons.
“Do explain your vision for the country, and what form of Brexit you want to see. But don’t pretend you will have the power to do everything you wish.
“In a political system in deep trouble for its failure to deliver, don’t set yourself up to be the next example of it.”