Tight end Jared Cook, meanwhile, will go elsewhere as a free agent, a source told ESPN's Rob Demovsky.
Shortly after the signing Friday night, Bennett tweeted his excitement over becoming a Packer.
— Martellus Bennett (@MartysaurusRex) March 11, 2017
"Watching the Pack last year -- I saw some things with Aaron Rodgers at quarterback and Jordy Nelson outside, Randall Cobb and all the talent on the team -- I thought it would be a great place for me to come in and just try to add on to what they already have," he said.
"It's always been one of the best places to play in the NFL with the fans, and the grass is always good there, which is a huge thing, as well. It's always been a hostile environment as an away team. It'll be good for them to be rooting for you instead of against you, because that crowd gets crazy."
The Patriots acquired Bennett in a trade with the Chicago Bears last March and inherited the final year of his contract, which called for a 2016 base salary of $5.085 million. The sides had discussed extending the contract through 2017 at the time but couldn't come to an agreement.
That set up Bennett -- who turned 30 on Friday -- to become an unrestricted free agent this offseason. He was widely viewed as the top tight end available.
The 6-foot-6, 265-pound Bennett totaled 55 receptions for 701 yards and seven touchdowns in the 2016 regular season, playing in all 16 games. He earned the respect of many of his teammates by playing through an ankle injury initially sustained on Oct. 9.
A supersized personality, Bennett was acquired with the hope of forming the NFL's most lethal 1-2 tight end combination alongside Rob Gronkowski. But that never truly materialized because Gronkowski was limited to just eight games because of hamstring and back injuries.
That thrust Bennett into a more consistent role as the team's No. 1 option at the position. He caught five passes for 62 yards in the Patriots' Super Bowl victory over Atlanta.
In late February, Gronkowski said of Bennett, "I'm hoping that he breaks the bank. Whenever you see a tight end break the bank, it's good for the industry, it's good for the position. You want to see the position grow."
Bennett was selected to one Pro Bowl, in 2014, when he posted career highs in receptions (90) and receiving yards (916) with the Bears.
Kendricks, a Milwaukee native and Wisconsin alum, played in all 16 of the Rams' games last season, making 50 catches for 499 yards and two touchdowns.
ESPN's Mike Reiss contributed to this report.