The Giants acquired quarterback Eli Manning, the No. 1 pick in the 2004 draft last week, and the 31-year-old Collins refused to accept a pay cut to stay with the team.
"Unfortunately, the economics of the system we work in today determine these most difficult decisions," General Manager Ernie Accorsi said.
Collins said he told Accorsi he didn't wish to become a backup quarterback.
"I also think it would've made things very awkward for Eli and I," Collins said.
Collins started 67 straight games for the Giants before missing three games at the end of last season with an ankle injury. In 2000, Collins threw five touchdown passes against Minnesota in the NFC championship game and the Giants went to the Super Bowl.
"His performance ... against Minnesota was one of the greatest in the history of the franchise," Accorsi said."
"I believe I've got a lot of good years left," Collins said.
Celebrity Breakups and divorces of 2014 [PHOTOS]