Dudley and the Suns agreed to a three-year, $30 million deal, his agent, Mark Bartelstein, told ESPN's Jeff Goodman.
Dudley revealed the news on his Twitter account, saying that he is "coming home" to Phoenix, where he played for five seasons.
A nine-year veteran, Dudley earned $4.25 million in 2015-16. That amount was via a player option he exercised last season before being traded to the Washington Wizards from the Milwaukee Bucks. He exercised the option knowing that back surgery was likely after suffering a herniated disk last July.
Dudley, 30, bounced back well from the surgery. Last season with the Wizards, Dudley played in 81 games, starting 41, and averaged 7.9 points, 3.5 rebounds and 2.1 assists in 25.9 minutes.
Dudley seemed to perform better as a starter. He made 45 percent of his 3-point attempts in games he started and hit 35 percent of his 3-point attempts in 40 games coming off the bench.
Late in the regular season, Dudley told the Washington Post that he'd be seeking a three-year contract and would be open to staying with the Wizards.
Information from ESPN.com's Ian Begley was used in this report