The move brings an end to the 31-year-old's nine-and-a-half year stint with the Midlands outfit, during which time he made 307 appearances, scoring 44 goals and winning both the Championship and League One titles.
Last season the Wales international was Wolves' joint-top scorer in the Championship, finding the net 10 times in the most prolific campaign of his career.
Following the arrival of Nuno Espirito Santo as Wolves boss this summer, Edwards fell down the pecking order and has now joined striker Jon Dadi Bodvarsson in making the move from Molineux to Jaap Stam's side.
Brian Tevreden, the Royals' sporting director, said: "I am very pleased to welcome a midfielder with proven Championship and Premier League pedigree into our group and, as a player who has been a key part in the cut and thrust of many campaigns with Wolves, I am confident he will be a valuable addition to the squad here at Reading."
Edwards will go into contention for his new side after spending the international break on Wales duty.