The Redskins and Bills also put in a claim for Babin, a source told ESPN, but the Jaguars were awarded the defensive end because they had the worst record (2-9) of the teams that made claims.
The Jaguars will pay the remaining $1.69 million of Babin's 2012 salary, essentially taking a low-risk look at someone who significantly could upgrade one of the league's worst pass rushes.
"It's a good pickup," coach Mike Mularkey said. "He's had a lot of success over the last three years and we could use some help in that area. He'll fit what we're doing. (Defensive line coach) Joe Cullen and he have a relentless type of mindset. I just think it's going to be good for us, really good for us."
The two-time Pro Bowl defensive end's release was the first major roster move for the Eagles, who have lost seven straight games.
Babin had just 5.5 sacks after recording 18 last year. He signed a five-year, $28 million deal last summer after going to his first Pro Bowl with Tennessee after the 2010 season.
Jacksonville has a league-low 13 sacks, a glaring weakness on a team filled with holes.
The Jaguars gave Jeremy Mincey a four-year contract worth $20 million in March, but he has two sacks. They also drafted Andre Branch in the second round, but he has played sparingly the past two months.
Babin will play Sunday at Buffalo, Mularkey said.
"We've got five games and we're trying to win these games," Mularkey said. "It's a sign that we're trying to show our team that we're trying to win right now, that this is not, 'Play the young guys and do the evaluating.' We're trying to win and we're doing whatever we can to improve our roster. This is a great move."
Babin might even start over Austen Lane, who missed practice Wednesday with a foot injury and is expected to sit out again Thursday.
"Let's start working him in the plan and see what we have to do to get him up to speed as quickly as we can," Mularkey said. "Can he play Sunday? Yes. I know he will. We're anticipating him playing."
Eagles coach Andy Reid said the Eagles cut Babin to give more playing time to younger players.
Information from ESPN NFL Insider Adam Schefter and The Associated Press was used in this report.