Wizards president Ernie Grunfeld announced the deal on Sunday. Anderson's agent, Mark Bartelstein, confirmed the terms of the contract on Tuesday.
The 6-foot-6 Anderson played the past two years with the Brooklyn Nets, averaging 7.4 points and 2.8 rebounds last season.
In Brooklyn's first-round playoff series against Atlanta last season, Anderson averaged 11.1 points and 3.5 rebounds while shooting 61 percent from the field.
He has spent a total of six seasons with three teams in the NBA, but also has played professionally overseas.