The 31-year-old agreed terms with the Royals late last night and the deal was announced shortly before Wolves' match against Brentford on Saturday afternoon.
The Welsh international becomes the second Wolves player to join Reading this summer after Jon Dadi Bodvarsson moved in a £3m deal last month.
In total Edwards played 306 times for Wolves, scoring 44 goals. He is 33rd on the club's all-time appearance list.
He has signed a two-year contract with Reading.
Their chief executive Ron Gourlay said: "It is always so important to strike the right balance between youth and experience within a squad and, with more than 500 career appearances to his name already - earned with both club and country - Dave adds experience in abundance to this group of players.
"And, crucially, he is hungry for more success as a Royal and we look forward to welcoming him to the club after he returns from international duty with Wales."
Reading sporting director Brian Tevreden added: "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."