Babin agreed to a two-year contract, a source confirmed to ESPN.com's Rich Cimini. The agreement includes a team option in the second year, NFL Network reported.
"You can't have enough pass rushers," coach Rex Ryan said as the team checked into training camp in Cortland, New York. "He is a relentless guy, (with) a phenomenal motor. Obviously, he's got a history of being able to get to the quarterback. He's going to bring a lot to the table in that regard, for sure.
"You watch the tape from last year, and he's got plenty left in the tank."
Babin is expected to join the team Thursday for its first practice.
The Jets play a 3-4 base defense, but they plan to use Babin as a situational pass rusher, especially when they go to a four-man front on passing downs. He also provides insurance in the event that linebacker Antwan Barnes, placed on the physically unable to perform list as he recovers from knee surgery, isn't ready for the season.
The Jaguars released him this offseason just three months after re-signing him to a three-year contract worth $7.275 million that included a $500,000 signing bonus.
The Jaguars claimed Babin off waivers from the Eagles in November 2012. He was scheduled to make $6 million in 2014 and '15, but he voided the final two years of his contract because of a rule in the new collective bargaining agreement that allows a vested veteran claimed after the trade deadline -- which the Jaguars did in 2012 -- to declare himself a free agent following the season in which he was claimed.
He has 62.5 career sacks.
The Jets released cornerback Lowell Rose to create a roster spot for Babin. Guard Willie Colon, who is recovering from arthroscopic knee surgery, and linebacker Antwan Barnes, whose 2013 season was ended by a torn ACL, were placed on the PUP list to begin training camp.
ESPN.com Jets reporter Rich Cimini contributed to this report.