The 6-foot-6, 32-year-old sharpshooting guard signed a one-year deal for the veteran's minimum of about $1.3 million.
Redd left the Milwaukee Bucks at the end of last season, the final year of his six-year, $91 million contract he signed with the Bucks in 2005. Injuries to his left knee cost him most of the last three seasons. Redd played in 33 games in 2008-09, 18 games in 2009-10 and 10 games in 2010-11.
"We came out and worked out on Tuesday," Redd said after the Suns practiced Thursday. "It went well. They wanted to see how I moved, if I still had some juice in the tank. I came out and performed and yesterday we made it happen."
He averaged 20 points in 11 seasons, all with the Bucks. A 38 percent 3-point shooter for his career, Redd's best season came in 2006-07, when he averaged 26.7 points per game.
"I want to play at the elite level that I'm accustomed to playing at," he said. "I asked all the doctors after this last surgery, 'Can I play at the level that I'm accustomed to playing at?' and they said, 'Yeah,' so that's the goal for me."
He said "more than anything" he wants to "have fun and play without pain."
The Suns' training staff has a reputation for having success in working with players who have dealt with injury, with the 39-year-old Hill the prime example.
"That was big," Redd said. "That was one of the things that really drew me to this organization was the fact that they have an incredible medical staff. I wanted to be a part of that to get better, but I feel great "
He said Hill talked to him and said that if he came to Phoenix, he could get back the years that he's lost to injury.
"I've seen his career rebirthed and hopefully the same can happen to me," Redd said.
Redd said he took off 14 months between his latest surgery and his return to the Bucks in April. By the time his legs began to feel in NBA shape, the season was over.
"When you go through something like this, it wears on you mentally more than anything," Redd said, "so I just want to get the mind right and obviously the body right."
He wasn't sure when he would be able to play in a game, but is working to get in shape to keep up with Steve Nash and the rest of the offense.
"He brings a guy that can obviously shoot the ball from deep, he's very good at getting his shot off on screen and rolls," coach Alvin Gentry said. "Hopefully, he'll add something to the team for us."
The normally prolific Suns have struggled mightily offensively in their first two games, shooting barely 40 percent from the field and just 19 percent from 3-point range. Starting two guard Jared Dudley is shooting 23 percent and his backup, Shannon Brown, 27 percent.
Suns president Lon Babby insisted the signing of Redd was "not in any way, shape or form" a reaction to those two games.
"It was something we've been talking about for a long time," Babby said.