The Green Bay Packers' free-agent drought is finally ending with an addition at perhaps their most needy position.

Free-agent tight end Jared Cook is in Green Bay on Monday and will sign with the Packers when he's passed his physical, according to FOXSports.com's Alex Marvez. Two other teams were in the mix, but the deal was actually reached last Thursday.

Cook, 28, played four seasons with the Titans before spending the last three with the Rams. He set career highs with 51 and 52 catches for St. Louis is 2013 and 2014 but slipped to 39 last season. Cook signed a five-year, $35 million deal to come to the Rams in 2013 but was released in February.

Packers general manager Ted Thompson is always slow to sign other teams' free agents, and this offseason has been no different. Cook will be the Packers' first outside signing, and he will fill what became a gaping hole in the team's offense last season. Starting tight end Richard Rodgers regressed in his second year and was exposed as not fast enough to be a No. 1 tight end when several of the Packers' top receivers were injured.

Cook has been somewhat inconsistent but has never played with a quarterback near the level of the Packers' Aaron Rodgers and is far more athletic than Richard Rodgers. With the draft light on tight ends, adding him was perhaps Green Bay's last chance to get a field-stretching option at the position.