Chester started all 64 of Washington's games over the last four years. He will be reunited with Kyle Shanahan, the former Redskins offensive coordinator who's beginning his first season with the Falcons under new coach Dan Quinn.
Atlanta's offense will deploy the same zone blocking scheme Shanahan used with Washington.
Chester was a second-round draft pick for Baltimore out of Oklahoma in 2006. He has started 111 of 137 career games.
The Falcons waived linebacker Derrick Malone Jr. to make room for Chester on the roster.