Frazier will back up Wizards All-Star point guard John Wall. This will be Frazier's third team since breaking into the league in 2014-15, with previous stops with the 76ers and Trail Blazers.
The Pelicans now have two picks in the second round, Nos. 40 and 52.
Last season for New Orleans, Frazier averaged 7.1 points and 5.2 assists in 65 games (35 starts).
Veteran Brandon Jennings, who came off the bench for the Wizards after being released by the Knicks last season, is an unrestricted free agent.