The reshuffle also saw Environment Secretary Therese Coffey step down, saying in her letter it is time to "step back", with former Health Secretary Steve Barclay replacing her.
Victoria Atkins has stepped into Barclay's old role in the Department of Health, while Richard Holden has replaced Greg Hands as party chairman.
Speaking ahead of the reshuffle, a No10 source told GB News that Rishi Sunak "wants a united team to deliver the changes this country needs for the long term."
McVey's key role is said to be leading the Government's anti-woke agenda, sources told the Sun, making her the Government's "Common Sense" chief.
In a brief statement after his appointment, Cleverly said: "It is an honour to be appointed as Home Secretary. The goal is clear. My job is to keep people in this country safe."
Asked if he wants to distance himself from the language used by his predecessor Suella Braverman, Cleverly told broadcasters: "I intend to do this job in the way I feel best protects the British people and our interests."