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The lure of playing with LeBron James made it possible for the Cavaliers to sign Miller.
The second year of the contract will be a player option for Miller, sources said.
Miller averaged 7.1 points and 2.5 rebounds, and shot 45.9 percent from 3-point range last season with the Memphis Grizzlies. It was the first time he played all 82 games in a season since his rookie year (2000-01) with the Orlando Magic.
Before his one-year run in Memphis, he spent three seasons with LeBron James in Miami, where he helped the Heat win two championships as a key reserve.
Miller had several choices in the free-agent market, including the Denver Nuggets and Dallas Mavericks, sources told Yahoo Sports. The Grizzlies turned to Vince Carter once Miller showed interest in joining the Cavaliers.
In 15 NBA seasons, Miller has averaged 11.8 points and 4.6 rebounds per game.
ESPN.com first reported Miller's agreement with Cleveland.