The agreement between the teams, first reported by the NFL Network and confirmed by ESPN, came after Stork had been informed by the Patriots that they planned to release him.
The Patriots also released veteran wide receiver Nate Washington on Wednesday. That move was first reported by CSN New England and later confirmed by ESPN.
The Patriots' decision to cut ties with Stork comes as a mild surprise even as he was losing his hold on the top spot of the depth chart to second-year blocker David Andrews.
Stork, who was selected by the Patriots in the fourth round of the 2014 draft, played in 25 games for the team, including the playoffs, during the past two seasons (21 starts). He sustained multiple concussions in that time, opening the 2015 season on the injured reserve list because of a concussion.
"It's tough," said quarterback Jimmy Garoppolo, who was picked by the Patriots in the same draft class as Stork. "It's that time of year. There's a lot of movement between teams and players and everything. It's tough to see one of your guys go like that. That's the business, I guess."
With Stork sidelined at the start of last season, Andrews, an undrafted free agent out of Georgia, started the first 10 games of the season and performed well before Stork returned as the starter.
Under returning offensive line coach Dante Scarnecchia, the two entered 2016 spring practices in an open competition for the job, with Stork taking top repetitions one day and Andrews getting those reps the next. That continued into the early days of training camp, but Andrews has has a hold on the top spot since Stork was knocked out of practice on the third day due to a reported concussion and missed a week.
When Belichick was asked about the center position Friday, he called it a "good competitive situation."
Washington, who has 458 career receptions in 10 seasons with the Steelers, Titans and Texans, was a longshot to make the Patriots' roster out of camp. He signed a one-year, $1.065 million contract with the Patriots this offseason, but only $60,000 was guaranteed.
Information from ESPN's Mike Reiss, Adam Schefter and Field Yates was used in this report.