The Washington Redskins and quarterback Rex Grossman have agreed to a one-year deal to bring back the nine-year veteran for a third season, Grossman confirmed Saturday night.

Grossman, 31, said he fully expects the Redskins to draft a quarterback with the second overall pick of the draft. But he said neither that likelihood, nor the possibility that the rookie could start from Day 1, discouraged him from wanting to return to Washington.

“I’m a firm believer in seeing things through, and I wanted to be a part of this team in any way possible regardless of what my role is, and help it get back on track,” said Grossman, who last season passed for 3,151 yards, 16 touchdowns and 20 touchdowns interceptions while completing 57.9 percent of his passes and posting a 72.4 quarterback rating.

Financial terms of the deal were not immediately known. It marks the third one-year contract that Grossman, who started 13 games in 2011, has agreed to with Washington. The Redskins offered him a multiyear deal last offseason, but he declined because he wanted to keep his options open. He earned a base salary of $810,000 last season.

The Indianapolis Colts appear set on taking Stanford’s Andrew Luck with the first overall pick, and that would position Washington to select Baylor’s Heisman Trophy-winning quarterback, Robert Griffin III.

“They’re definitely taking a quarterback with the second pick of the draft,” Grossman said. “It’ll probably be RGIII, unless for some unexpected reason the Colts take him. But whether it’s RGIII or Luck, either way, I know that quarterback is going to be the franchise quarterback at some point. Like I said, I just want to be a part of this team. Whether it’s helping that guy get ready to play, or whether it’s playing until he is ready to take over, I just want to help out in whatever way it is.”

Despite trading up to take a quarterback, Washington still sought a veteran, and had interest in signing Kyle Orton, according to people of knowledge of the situation. But Orton agreed to terms with Dallas last week. The Redskins soon after turned their attention to working out another deal with Grossman.

Redskins coaches respect Grossman’s ability to make throws under pressure. Grossman also has a firm understanding of the offense, having played for offensive coordinator Kyle Shanahan for three seasons (two in Washington and one in Houston).

Grossman said that he had another team interested in him, but turned down that opportunity because he wanted to remain with the Redskins, and liked the familiarity he has with the coaches and the system. He declined to say which team he was considering.

Whether he starts or serve as a backup to the rookie, Grossman believes he can play better than what he did last season.

He beat out John Beck for the starting quarterback job in Week 1 of last season, and got the nod in the first five games, going 3-2 during that stretch. He was benched in Week 6 after throwing four interceptions against the Philadelphia Eagles.

Beck started the next three games but struggled mightily. Grossman reclaimed his job and helped reignite a sputtering offense, but Washington went 2-6 down the stretch of the season.

In addition to his 20 interceptions, Grossman lost five fumbles, and he’s well aware that his turnover problems are crippling. But, he believes they are correctable.

“I need to and can get better with consistency,” Grossman said. “I can go out and play lights-out one week, and the next week, not do so well. The number-one thing is turnovers. I’ve got to do better with decision-making, and things like that, and I think I can.”

More on the Redskins and free agency:

Tackle Eric Winston signs with the Chiefs

P. Manning works out for Titans; decision time approaches

Latest Redskins updates on The Insider