The Scot, 48, returns to Boundary Park for a fourth spell, twice as a player, and now twice as an assistant manager.
He was most recently with Latics in 2009 and then worked with John Sheridan at Chesterfield.
It was with the Spireites when Johnson first worked with Wright, and the manager said: "He's a good guy. Everyone knows him and likes him here, he's got an affinity with the club and I'm looking forward to working with him."
- Sports & Recreation