The 25-year-old former Wrexham man enjoyed an influential season as he scored seven goals in 39 appearances for Jim Bentley's side.
Budgetary restraints have seen influential duo Nick Fenton and Will Haining released by the Shrimps, so Bentley is delighted to have secured Fleming's services.
"Andy has had a great season and has all the credentials needed to be one of the best midfielders in the Football League," he told the club's official website.
"There has been interest from other clubs in him and I am delighted that he has agreed to join us again.
"He is a big player for us and a big signing and I'm sure he will just get better and better."