Gortat and guards Shannon Brown, Malcolm Lee and Kendall Marshall head to Washington in return for the expiring contract of 2004-05 Rookie of the Year Emeka Okafor and a protected 2014 first-round pick (to No. 12).
Following the move, Gortat tweeted: "I knew it [was] gonna happen so Im glad it happened now not in mid season.! Its still hard to leave such a great city."
The 29-year-old, who stands 6'11" tall, averaged 11.1 points and 8.5 rebounds per game last season for the Suns.
The Wizards begin their season with a trip to Detroit on Wednesday night.