The Falcons have reached a one-year contract with quarterback Rex Grossman on Wednesday.

He took a physical and worked out for the team on Tuesday.

Last week, a report surfaced that Grossman turned down an offer from the Jets because he wanted to reunite with Falcons offensive coordinator Kyle Shanahan and play for the Falcons. He played for Shanahan in Washington and was with him in Cleveland last season before being released.

Grossman, the former Florida Gator, has not played in an NFL game since 2011.

The Falcons were not interested originally because they were pleased with T.J. Yates and Sean Renfree. But after both Yates and Renfree struggled against the New York Jets’ reserves, the team had a change of heart.

Grossman, 35, was drafted 22nd overall by the Chicago Bears in the 2003 draft. He has started 47 games over his career and helped the Bears reach Super Bowl XLI, where they defeated 29-17 by the Indianapolis Colts.

Grossman also spent time with Houston (2009) and Washington (2010-13).

Matt Ryan hasn’t missed a game since the 2009 season and his streak of 87 starts in a row is the fifth-longest among active quarterbacks, despite playing under severe duress the past two seasons.

Over his career, Grossman has completed 863 of 1,562 passes (55.2 percent) for 1,562 yards, 56 touchdowns and 60 interceptions.