Wilcox, 27, was vying for a third spot on the depth chart in Foxborough behind veterans Hunter Henry and Austin Hooper.
The 6-foot-4, 250-pound tight end entered the league with the Cincinnati Bengals as an undrafted free agent in 2020.
A 53-man roster promotion came late in the rookie campaign for Wilcox, who caught 29 passes for 211 yards and one touchdown.
Wilcox, who was not tendered as a restricted free agent in March, stayed sidelined during the preseason finale after being limited in practice.
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