Pickett left Buffalo on Tuesday without a contract and has been mulling an offer from the St. Louis Rams for a number of days.
The Packers met with Pickett on Monday and he signed a multi-year deal today, according to the ESPN report.
Pickett, 26, was offered a five-year, $16 million deal by the Rams, according to the St. Louis Post-Dispatch. It is likely that Green Bay's offer is similar, and probably more for the former Ohio State Buckeye. Terms were not immediately available.
Pickett now is expected to replace Grady Jackson as the run-stopping defensive tackle in the team's 4-3 scheme. In five seasons with the Rams, Pickett has six sacks in 75 games. He led the Rams' defensive linemen with 65 tackles last season, and had two sacks.
Pickett's signing comes after the Packers signed UFA safety Marquand Manuel and re-signed running back Ahman Green and defensive end Aaron Kampman last week.
The Packers were thought to be highly interested in Seattle defensive tackle Rocky Bernard, but the Seahawks re-signed him today to a three-year deal worth $13.5 million, including a $5.5 million signing bonus.
The 33-year-old Jackson is an unrestricted free agent, but has yet to visit with any other teams.