The Patriots also waived wide receiver Darren Andrews.
The 29-year-old Allen spent the previous two seasons with the Patriots and had 13 catches for 113 yards and a touchdown with the team. New England acquired him in a trade with the Indianapolis Colts on March 9, 2017. The Colts originally selected him in the third round of the 2012 NFL Draft.
Allen has played in 86 games (71 starts) in his seven-year NFL career and has 139 receptions for 1,564 yards and 20 touchdowns. His best season came in 2012 with the Colts, when he had 45 catches for 521 yards and three scores.
Allen has seen action in 10 postseason games (four starts) and has 15 receptions for 141 yards and a touchdown.
The 23-year-old Andrews signed with the Patriots as an undrafted free agent out of UCLA on May 11, 2018. He spent his rookie season on the reserve/non-football injury list.
Andrews had 162 receptions for 1,977 yards and 15 touchdowns during his collegiate career with the Bruins. He is fourth on the school's all-time receptions list.