Griffin has accepted the job, sources on Monday told ESPN The Magazine's Ric Bucher, several weeks after turning down the Denver Nuggets' offer to be their general manager.
A league source told Bucher at the time that Griffin, who resigned as the Suns' senior vice president of basketball operations when general manager Steve Kerr left in June, declined the Nuggets' offer in part because it was nowhere near $1 million a year, the median salary for recently hired GMs that include the Cavaliers' Chris Grant.
Grant was hired in June after the Cavaliers didn't bring back Danny Ferry. Byron Scott then joined the Cavaliers as head coach to replace Mike Brown, who was fired in May. Also, vice president of basketball operations Lance Blanks resigned to become Phoenix's GM.
Cleveland finished the regular season 61-21 as James garnered his second consecutive NBA MVP award. But the Cavaliers were ousted in the second round of the playoffs by the Boston Celtics in six games.
Information from The Associated Press was used in this report.