Anderson's agent, Mark Bartelstein, confirmed the terms of the deal on Tuesday.
Teams cannot sign deals with free agents until Thursday.
The 6-foot-6 Anderson played the past two years with the Brooklyn Nets, averaging 7.4 points and 2.8 rebounds last season.
He has spent a total of six seasons with three teams in the NBA, but also has played professionally overseas.
Anderson, 32, represents the latest new face for a Wizards team that reached the second round of the playoffs last season. Washington also is adding Gary Neal via free agency, Jared Dudley via a trade, and Kelly Oubre Jr. via the draft.