Dutch was undrafted out of Michigan last year and spent time on the Redskins' practice squad. The 5-foot-11, 199-pound Dutch was signed to a reserve/future contract in January.
Beck says he told Ravens coach John Harbaugh he is excited about the move, but it's tough to leave Baltimore because "this is a special football team."
Baltimore has placed injured cornerback Domonique Foxworth on injured reserve, after he suffered a season-ending knee injury last week.
Beck is a former Miami Dolphins second-round draft pick from Brigham Young.
Dutch, 24, is a Washington native and former standout at Gonzaga High School.