The Clippers acquired Miller and shooting guard Bryant Stith, while sending athletic forward Darius Miles and forward Harold Jamison to the Cavaliers.
The reigning league leader in assists, Miller dished out 10.9 helpers while scoring 16.5 points with 4.7 rebounds.
The 26-year-old, who will be entering his fourth year out of Utah, has started all but one game in the last two seasons with the Cavs.
For his career, he has netted 14.5 points and added 8.2 assists a game.
Miller has missed just one of a possible 246 games over his career.
The 20-year-old Miles, a 6'9" forward, will bring his acrobatic skills to a Cavaliers club which finished in seventh place in the Central Division last year with a 29-53 record.
Miles averaged 9.4 points and 5.7 boards in 26.7 minutes over two seasons with the Clippers.
"It?s always difficult to trade a very exciting and popular player with potential such as Darius," stated Clippers vice president of basketball operations Elgin Baylor.
"The one thing that makes this both easier and exciting is a situation like this when you are getting a proven player in return who has established himself as one of the top five point guards in the NBA.
"In Andre Miller we feel we are getting the precise player we need to take our team to the next level. That made this hard decision easier to make."
This is the second consecutive year that the Clippers were involved in acquiring a franchise player.
Last season, the club acquired Elton Brand from Chicago in exchange for its No. 2 pick, Tyson Chandler, in a draft night trade.
Stith, a 10-year veteran out of Virginia, averaged 4.2 points and 1.7 rebounds per game last year with Cleveland.
Drafted by Denver in 1992, he played eight seasons with the Nuggets, before joining Boston for the 2000-01 campaign.
Stith has averaged 10.1 points and 3.4 rebounds over his career.
Jamison, who has two years of NBA experience, averaged 2.2 points and 1.6 boards in 25 games last year with the Clippers. The North Carolina product played his rookie season with the Miami Heat, where he only played in 12 games.