The Wizards announced the deal on Wednesday. ESPN.com reported on Aug. 23 that an agreement between the team and Webster was in place.
Webster played with the Minnesota Timberwolves last season, averaging 6.9 points and 3.6 rebounds.
The 6-foot-7 Webster is averaging 8.4 points and 3.2 rebounds in a seven-season NBA career with the Portland Trail Blazers and Timberwolves. He has shot 37.4 percent on 3-pointers.
Webster was the No. 6 overall pick in the 2005 draft after leaving high school.
Information from The Associated Press was used in this report.