Mr Hancock had been a minister in successive Conservative governments since 2013 and served as health secretary during the coronavirus pandemic.
In June 2021, he was forced to resign from the role after he breached social distancing guidelines by kissing a colleague.
Despite supporting Mr Sunak in the Conservative leadership campaign, Mr Hancock wasn’t given a role in government when the prime minister entered Downing Street.
The MP subsequently joined the cast of I’m A Celebrity – a decision that attracted criticism from his fellow MPs and local Conservative association.
Announcing his decision to quit Parliament, Mr Hancock said: “There was a time when I thought the only way to influence the public debate was in Parliament, but I’ve realised there’s far more to it than that.
“I have increasingly come to believe that for a healthy democracy we must find new ways of reaching people – especially those who are disengaged with politics.
“The revival of modern conservatism over the next decade will I suspect take place as much outside Parliament as in it.”