The former Defensive Player of the Year told The Associated Press on Sunday he heard from a lot of teams, but agreed to a two-year deal to stay with the Pistons about a week ago.
"This is the place I want to retire," Wallace said in a telephone interview with the AP.
Wallace, who expects to take a physical soon, will make $1.9 million each season.
The 35-year-old Wallace was one of Detroit's best players last season when it endured a miserable, injury-plagued year and didn't make the playoffs for the first time since 2001.
Dumars has said he intends to be active this offseason, and Wallace is confident he isn't coming back to a losing team.
"When we're healthy, we're pretty good," he said. "If we stay healthy and improve, I think we'll be able to compete."
While several of his teammates went down with various injuries, Wallace didn't miss a game last season until March. He then missed several games toward the end of the year with sore knees.
Dumars acquired Wallace as part of the Grant Hill sign-and-trade deal with the Orlando Magic a decade ago. Wallace helped spark the franchise's turnaround, culminating with the 2004 NBA title. He won the Defensive Player of the Year award four times in a five-year span.
The 6-foot-9 Wallace became the shortest player to lead the league in blocks during the 2001-02 season when he also led the league in rebounding. He is part of an elite group of players who have led the NBA in both categories in a single season, a list that includes Orlando's Dwight Howard, Hakeem Olajuwon, Kareem Abdul-Jabbar and Bill Walton.
In the summer of 2006, he took advantage of his value on the market and signed a $60 million, four-year deal with the Chicago Bulls.
It worked out for him financially, but not on the court.
The Suns didn't want Wallace and bought out his contract. After contemplating retirement last year, Wallace signed a $1.3 million, one-year deal with Detroit.
Wallace was suddenly rejuvenated, feeding off the fans who regard him as one of the most popular players in Detroit sports history, and looked like his old self at times.
After he had 16 rebounds -- seven offensive -- three blocks and three assists in a win over Philadelphia, Pistons coach John Kuester acknowledged he didn't expect Wallace to do much more than tutor the team's young post players.
"I never imagined he could have this kind of impact on the court," Kuester said after the standout performance in November. "This is the old Ben Wallace again."
Wallace, of White Hall, Ala., averaged 5.5 points, 8.7 rebounds and 1.2 blocks last season.
Wallace went undrafted after playing his college ball at Virginia Union. He was with Washington for his first three seasons and Orlando for one before he was acquired by Detroit.
He has never averaged more than 9.7 points a game in any season, but developed a niche in the league as a player who could defend guards or centers, block shots, rebound and pass.