Knighton tweeted Thursday that he had made a decision, then later sent out a picture of himself wearing a Patriots helmet.
New England has been searching for veteran depth at defensive tackle after two of its top backups last season, Akiem Hicks (Chicago Bears) and Sealver Siliga (Seattle Seahawks), signed elsewhere in free agency.
The Patriots return starters Malcom Brown (2015 first-round pick) and Alan Branch (11th year) at defensive tackle. New England also has Chris Jones (fourth year), Dominique Easley (third), Frank Kearse (fifth), Ishmaa'ily Kitchen (fourth) and Joe Vellano (third) on the depth chart.
The 29-year-old Knighton spent 2015 with the Washington Redskins after signing a one-year deal with incentives. He met with the Redskins earlier this week but left without signing a contract.
He played in the Redskins' base 3-4 package as a nose tackle and in their nickel package as an interior rusher. Knighton finished with 29 tackles, including 17 solo, and 1.5 sacks in the regular season.
Jacksonville selected Knighton in the third round out of Temple in the 2009 draft. Knighton spent his first four seasons with the Jaguars before signing with Denver in March 2013. He spent the next two years with the Broncos before joining Washington.
Knighton has 14 career sacks, 7.5 of which took place with Jacksonville.
He played in 15 regular-season games with Washington in 2015, missing a game at New England because of a rare condition called cluster headaches.
ESPN.com's Mike Reiss and John Keim contributed to this report.