The Falcons released tight end George Cooper, who was signed on Aug. 4.
Pollard, a 14-year veteran, was released by New England on Wednesday. He has 349 career receptions for 4,280 yards and 40 touchdowns in 13 seasons, most with Indianapolis. He led Seattle tight ends with 28 catches for 273 yards last season and signed with New England as a free agent in April.
Pollard spent 10 seasons with Indianapolis (1995-2004).
In 2001, Pollard set career highs with 47 receptions, 739 receiving yards and eight touchdowns.