"For me, it's a no-brainer," the 33-year-old shooting guard said. "I was chomping at the bit to come back here and play. It doesn't hurt that I got a good deal."
Bell signed a three-year deal Monday worth about $10 million.
The 6-foot-5 Bell was a favorite with fans and coach Jerry Sloan because of his defense. He had two breakout seasons with the Jazz but left in 2005 to take an offer from Phoenix that he said was too good to pass up.
Bell is a career 41 percent 3-point shooter who has averaged more than 10 points per game while playing for six different teams. He spent last season with Charlotte and Golden State, but played in just six games because of wrist surgery.
Bell said his left wrist has fully recovered.
General manager Kevin O'Connor noted that Bell made a good business decision when he took a "lucrative" offer from Phoenix while the Jazz were in a rebuilding phase.
"Now he's made an even better decision," O'Connor said. "We're really happy to have somebody back as competitive and as caring about wins and losses as our head coach is, and they have a relationship that goes a lot deeper than most."
The Jazz needed a shooter after free agent Kyle Korver signed two weeks ago with the Chicago Bulls, who had also just signed power forward Carlos Boozer. Utah replaced Boozer with the bigger, younger Al Jefferson and the Jazz will have shooters in Bell, first-round draft pick Gordon Hayward and C.J. Miles.
"We felt like when we lost a couple of players, we needed some three-point shooting," O'Connor said of Bell. "We got a guy who shot 41 percent for his career, and we needed some perimeter defense, and we got a guy that's done a terrific job all throughout his career from a defensive standpoint. We feel we got two-in-one."