Pennington, a first-round pick by the Jets in the 2000 NFL draft out of Marshall University, is the league's all-time leader in completion percentage at 65.6 percent (1,259-of-1,919), but had faced ongoing fan criticism for his lack of arm strength.
Before the 2006 season, he overcame two rotator cuff surgeries to lead the Jets to the playoffs and win the NFL's Comeback Player of the Year award.
"I have all the respect in the world for Chad as a person and a player," said Jets general manager Mike Tannenbaum on the team's Web site. "We have accomplished a lot of great things with Chad, including winning playoff games, which is very hard to do. He gave his heart and soul to this organization for a long, long time."
Favre is the team's likely starter this season.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys