Edwards was recently released by City, but played for Colchester's reserves in their 5-0 win over Swindon on Wednesday.
The 22-year-old defender made a good impression, and U's manager Phil Parkinson has given him a contract until the end of the season to get a better look at him.
He said: "Although he is still young, Mike has a great deal of experience for his age.
Edwards Extends Trial
"He played as a centre-half for the reserves on Wednesday, but he can play anywhere across the back line. He gives us extra cover, which I felt we needed.
"It's a big chance for Mike. I've signed him until the end of the season, but he must be looking to impress, with regards getting a long-term contract."