The Brexit minister is the 11th candidate to confirm they are running, after Theresa May announced she would stand down on 7 June.
The winner, expected to be named by late July, will also become prime minister.
In an open letter, Mr Cleverly set out his case to become leader and said he had backed Brexit from the beginning.
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He said: “I have never been blind to the complexities of the process and I have always been uncomfortable with those who offer artificially simple solutions.”
The MP for Braintree in Essex spoke about the need to unite the party, arguing: “We cannot bring the country back together unless the party of government is united, and the party cannot unite if it is led from its fringes.”
He also called for change, writing: “To inspire the British people we need to look different, sound different, and offer something new. I believe I can do that.”
Speaking at a summit of EU leaders in Brussels on Tuesday, Mrs May urged her successor to seek a consensus on Brexit in Parliament.
Senior EU figures at the summit reiterated that the agreement they secured with the UK could not be reopened.
Some of the leadership contenders have indicated that they could consider leaving the EU on 31 October without a deal with the bloc – but others say that would be unacceptable.
Who is standing?
Along with Mr Cleverly, the confirmed candidates to replace Mrs May are:
- Environment Secretary Michael Gove
- Health Secretary Matt Hancock
- Foreign Secretary Jeremy Hunt
- Home Secretary Sajid Javid
- Former Foreign Secretary Boris Johnson
- Former Leader of the House Andrea Leadsom
- Housing minister Kit Malthouse
- Former Work and Pensions Secretary Esther McVey
- Former Brexit Secretary Dominic Raab
- International Development Secretary Rory Stewart
The deadline for Tory MPs to put their names forward for the leadership race is the week commencing 10 June, and they must have at least two of their colleagues supporting them.
Once the deadline passes, there will be a series of votes by MPs on which candidate they prefer.
Each round will see the MP with the least number of votes struck off the list, until there are only two candidates left.
These two MPs will then be voted on by members of the Conservative Party to choose the next leader – and next PM.
All candidates in the race by mid-June will be invited to a hustings event on BBC One and the final two will go head-to-head in a Question Time Special.