The 24-year-old has previously worked with Dons boss Neal Ardley at Cardiff City and will now link up with the League Two side after recovering from a long-term knee injury.
Ardley told the club's official website: "I coached Aaron when I was at Cardiff, where he came through the ranks. When he first joined, he was a central midfielder, but I noticed that no-one could beat him in one-on-one situations so I played him at full-back.
"He was outstanding and managed to make the first-team squad at Cardiff. He played in central midfield for Aldershot last season and I know that they were very disappointed to lose him when they were fighting relegation.
"Aaron can play in a number of positions, but he can be a very good centre-back in my eyes. When he suffered an ACL injury I sent him my best wishes and said there could be something here for him if he got strong again."
Morris was released by Aldershot in the summer.