The 22-year-old, who has previously spent two loan spells at Huish Park, had made four appearances for the Robins since becoming a professional with the npower Championship side in 2009.
Edwards had spent loan spells with Bath City and Stockport before two separate stays at Yeovil, both in 2012.
"I am really pleased that Joe has signed for Yeovil Town," manager Gary Johnson told the club's official website.
"It is far better playing first-team football for a lower league team than sitting on the bench and getting no football.
"I believe Joe has a great future and I am very happy that Joe has chosen to further his career at Huish Park."
Edwards will go straight into the squad to play Preston on Saturday.
- Sports & Recreation
- Yeovil Town