In a post on X, he said: "I'm running to be Conservative Party Leader. Here's why..."
In a short video attached to the post, Mr Cleverly spoke of his upbringing in southeast London, where his mother was a midwife and his father ran his own business.
He said: "We need to re-establish our reputation as the party that helps grow the economy, helps people achieve their goals, their dreams and their aspirations.
"We can only do this as a united party focused on the needs of the British people, relentlessly working to make their lives better. If we do that, we can once again restore the confidence of the British people in us as a party.
"That is why I am putting myself forward to be leader of the party, to make sure this party, once again, is properly able to serve the British people."
He is the first to publicly declare his bid after securing the backing of the 10 Tories needed to make it into the first round.
Elsewhere, he took a swipe at potential rival Suella Braverman, who claimed that the party is full of "centrist cranks".
Mr Cleverly said: "Trying to carve up and divide up and factionalise is the wrong way of thinking."
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