Both QBs had strong pre-season moments but the Redskins will turn to the more experienced Grossman to open their campaign against the New York Giants on Sunday.
"It was a very close battle. I have a lot of faith in both of them and it has been very competitive all the way through, but I wanted to announce it and the starting quarterback will be Rex," Shanahan told the team's website (redskins.com).
"All-in-all, I thought he did a great job. I thought John did well too, but I thought Rex won it by an edge."
Beck has played sparingly in the NFL and has not reached the field since 2007. He will begin the season as the backup.
(Writing by Jahmal Corner in Los Angeles; Editing by Ian Ransom)