The signing were announced Thursday, shortly before the Falcons faced the Baltimore Ravens in the final preseason game.
Hayden spent the last six years with the Indianapolis Colts before being cut in a salary cap move. He has nine career interceptions and is best remembered for the pick he returned for a touchdown in the 2007 Super Bowl, clinching a 29-17 win over Chicago.
Sanders started 49 games for New England over the last six years, making eight interceptions and returning two of them for TDs. Last season, he set careers highs with three picks and six passes defended but, like Hayden, was cut for cap reasons.