[UPDATE: It is a two-year deal, according to NFL Network's Kimberly Jones.]
This is an interesting move for several reasons. For one, Babin is moving to outside linebacker in a 3-4 defense, a role that he has very little experience with in the NFL. At 34, the journeyman has to learn a new system and a new position. On top of that, Babin is joining a team that features Marty Mornhinweg as offensive coordinator. Mornhinweg was on the Eagles staff when Babin was cut in the middle of the season, so he was obviously asked about Babin before the signing.
Another former co-worker on the team is Michael Vick, who seemingly has become a leader in the locker room. Babin's reputation seemed to be spoiled after he was cut from the Eagles, as a flood gate of bad press followed about his personality and teamwork (or lack there of). For the Jets, this is likely a desperation move that makes little long-term sense, but will help them with depth this season.