The Falcons released the 34-year-old Abraham, who led the team with 10 sacks in 2012, on March 1.
With the 31-year-old Umenyiora, the Falcons have a slightly younger replacement at defensive end. Umenyiora had only six sacks for the Giants in 2012. He had a career-high 14½ sacks in 2005, but has reached double figures in only one of the last four years — 11½ in 2010.
Umenyiora, a two-time Pro Bowl selection, was a second-round pick by New York in 2003.
Terms of the deal weren't released. Umenyiora's agent, Tom Condon, couldn't be immediately reached for comment.
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