Kafka was released Friday afternoon, leaving Edwards and rookie Nick Foles behind Michael Vick on the depth chart.
"There was great competition at the quarterback position," Eagles coach Andy Reid said. "That's what football and training camp is all about. In the end, we had to make the difficult decision to let Mike Kafka go. Mike is a class act, a student of the game and a great person and I think he'll have no problem finding a job in the National Football League very soon."
Kafka, a fourth-round pick out of Northwestern in 2010, appeared in four games last year. He completed 11 of 16 passes for 107 yards with two interceptions. Kafka played in one preseason game this summer before breaking his non-throwing hand.
Edwards, a 28-year-old veteran, had an impressive month after sitting out 2011. He completed 54 of 80 passes (68 percent) for 489 yards, with four touchdowns and no interceptions.
Edwards started 32 games for Buffalo and one for Jacksonville in four seasons, going 14-19. He completed 60.5 percent of his passes for 6,019 yards and 26 touchdowns and 30 interceptions. He was released last preseason by Oakland and didn't find a job until the Eagles signed him in February.
"I'm proud of the way Trent Edwards conducted himself since the early days of the offseason workouts," Reid said. "He had to fight for everything he earned this summer. He improved each and every day and made the most of every opportunity."
Foles, a third-round pick from Arizona, was outstanding in the preseason. He finished 40 for 63 for 553 yards with six touchdowns and two interceptions for a 110.1 passer rating.
Veteran defensive backs Joselio Hanson and O.J. Atogwe were among 19 other players released.
Hanson spent the last six seasons in Philadelphia and was the team's nickel cornerback. Atogwe signed as a free agent in the offseason, but couldn't crack the starting lineup at safety.
Wide receivers Chad Hall, Mardy Gilyard and Marvin McNutt and linebacker Keenan Clayton are other notables on the cut list. The Eagles still must make two more moves to reach the 53-player limit.
Tight ends Brett Brackett and Chase Ford, defensive tackles Ollie Ogbu, Frank Trotter and Landon Cohen, fullback Emil Igwenagu, tackle D.J. Jones, linebackers Adrian Moten and Ryan Rau, defensive end Monte Taylor, safety Phillip Thomas and offensive linemen Steve Vallos and Brandon Washington also were released.