It will be Liverpool's 12th loanee departure this season and the midfielder's second successive campaign away from Anfield after spending some of the 2021/22 season with hometown club Blackburn.
Clarkson, an England Under-20 international, played seven times for Rovers last term and has made three senior appearances for Liverpool.
Dons manager Jim Goodwin told the club's website: "Leighton has had a very high standard of coaching within the LFC Academy and he has already represented Liverpool at first-team level in the FA Cup and Champions League.
"He is a ball-playing midfielder who always makes himself available as an option for his team-mates.
"He's brave in possession and, at the right times, is willing to try the difficult pass which some midfielders don't always have the ability or courage to attempt. That is something we will continue to encourage.
"We're very grateful to Liverpool for their assistance in making this loan possible."