The four-year, $17 million deal with a player option for a fifth year takes effect next season. That would keep the fan-favorite Dudley under contract until at least the 2014-15 season and possibly the next one as well.
New Suns president of basketball operations Lon Babby called Dudley "a valued member of what makes this franchise special."
The team announced the signing Friday night, the first significant move of the new front-office regime set up after Steve Kerr chose not to stay on as general manager.
Babby, a former agent, said it is difficult to negotiate long-term deals with the NBA labor situation so uncertain.
"I feel pleased because he's the kind of player and person that makes this franchise," he said. "It was challenging to get it done in this environment but hard work and good faith prevailed."
Dudley will get $4.25 million each season, beginning in 2011-12.
The scrappy, 6-foot-7 player from Boston College and 2007 ACC player of the year was drafted by Charlotte as the 22nd selection overall.
Richardson was considered the big prize in the Charlotte trade, with Dudley something of an add-on. But Suns coaches had heard of the player's potential and he meshed perfectly with Phoenix's up-tempo, rhythmic style.
He had a breakout 2009-10 season with career bests in virtually every category. He averaged 8.2 points, 3.4 rebounds and 1.5 assists while playing in all 82 regular-season games and all 16 playoff contests.
One of the team's best defensive players, Dudley led the Suns in steals with 81.
But he was noticed mostly from 3-point range, where he was the most accurate of the array of sharpshooters assembled by the Suns. He led the team by making 45.8 percent, fourth-best in the NBA.
In his first three NBA seasons Dudley made 38 3s. Last season, he made 120.