Atlanta lost linebacker Sean Weatherspoon for the season with a torn Achilles in June.
Angerer, a second-round pick by Indianapolis in 2010, made nine starts in 2013 and had 63 tackles with one interception.
Angerer finished last season on injured reserve with a knee injury. He made only three starts in 2012 because of a foot injury.
The Falcons also signed wide receiver Jeremy Ebert, who had three catches for 18 yards in five games with Jacksonville last season. Ebert was a seventh-round pick by New England in 2012. He spent time on the Patriots' and Eagles' practice squads in 2012.
Terms of Tuesday's deals were not released by the team.
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