"We worked out a deal yesterday," Montgomery told the newspaper. "I'm definitely happy to stay with the Redskins and for the chance to build on what we've started. I feel like we're only a few pieces away. We definitely have the talent, having beaten the Giants twice this year."
The newspaper did not report terms of the agreement. Montgomery was scheduled to become a free agent next month.
Montgomery, 29, spent his four seasons in the league as a backup before starting every game in 2011, his third with the Redskins. He played in 29 games for Washington the previous two seasons, including nine starts.
Montgomery was selected by the Carolina Panthers in the seventh round of the 2006 NFL Draft and played just six games with them that season, starting four, and played the next two seasons with the New York Jets.