The deal, which also sends guard-forward Jared Dudley from the Suns to the Clippers, had been reported earlier but could not be officially announced by the teams until Wednesday under NBA rules. The Milwaukee Bucks obtained two second-round draft picks as part of the trade.
Redick was acquired in a sign-and-trade deal with the Bucks. He was acquired by Milwaukee from Orlando in February and averaged 12.3 points per game in 28 games with the Bucks. He gives newly re-signed point guard Chris Paul a much-needed shooting option. Redick, who has played seven seasons in the NBA, has a career average of 9.4 points per game with the Magic and the Bucks.
Milwaukee gets the 2015 or 2016 second-round pick from the Clippers with protection or the 2017 pick without protection. The Bucks get the 2014 second-round pick the Suns had obtained from Toronto.
Bledsoe was Paul's backup with Los Angeles, averaging career highs of 8.5 points, 3 rebounds and 1.43 steals last season. In 12 starts, Bledsoe averaged 14.2 points, 4.8 rebounds, 5.3 assists and 2.5 steals. He scored a career-best 27 points at Orlando on Feb. 6.
Butler, a two-time NBA All-Star, is entering his 12th NBA season. He has a 15.5 point career average in 697 starts with Miami, the Los Angeles Lakers, Washington, Dallas and the Clippers.
Dudley was one of the most popular Phoenix players. When the trade first was reported, he tweeted that he hated to leave Phoenix but if he had to go he was glad it was to the Clippers.
New Suns general manager Ryan McDonough called Bledsoe and Butler "key parts of the Clippers team that set a franchise record for wins last season."
"We are excited to add their athleticism, shooting and leadership to our organization," he said.
Phoenix, with a new general manager and a new coach in Jeff Hornacek, are undergoing a major rebuilding job following the second-worst season in franchise history.
The team drafted 7-foot-1 centre Alex Len as the fifth overall pick last month, then added 18-year-old guard Archie Goodwin with the 30th overall pick.