The Miami Dolphins released Van Noy last week, just one season after signing him to a four-year, $51 million contract. The team tried unsuccessfully to trade the linebacker before releasing him.
Van Noy, who played both inside linebacker and edge rusher for the Dolphins, had 69 tackles and six sacks for the Dolphins in an up-and-down 2020 campaign.
Van Noy received a two-year contract with a maximum value of $13.2 million from the Patriots, a source confirmed to ESPN.
The Patriots have focused heavily on the front seven in free agency, having reached agreements with Dolphins defensive tackle Davon Godchaux, New York Jets defensive lineman Henry Anderson and Baltimore Ravens outside linebacker Matthew Judon, while re-signing defensive lineman Deatrich Wise Jr.
A combination of Van Noy and Judon on the edges of the defense could help address one of the Patriots' big struggles from 2020.
The Patriots' run defense ranked 26th in the NFL last season, with opponents averaging 131.4 rushing yards per game. In addition, opposing rushers averaged 4.5 yards per carry.
A second-round draft pick of the Detroit Lions in 2014, Van Noy established himself as a starter after being traded to the Patriots in 2016. In four seasons with the Patriots, he had 16.5 sacks, 5 forced fumbles and 221 tackles. He also was a part of two Super Bowl-winning teams.
Van Noy, 29, has 358 tackles, 23.5 sacks, 7 forced fumbles and 2 interceptions in 95 regular-season games over seven seasons.
Allen, who had signed a two-year, $7 million deal (with $2.75 million guaranteed), didn't play for the team last year due to injury, while Lee was one of eight players to opt out of the 2020 season.
ESPN staff writer Cameron Wolfe contributed to this report.