Arbitrators Gary Kendellen, Brian Keller and Allen Ponak made the decision Wednesday, a day after hearing arguments.
A 31-year-old right-hander, Greene was a first-time All-Star last year, when he made $4 million.
He had a 2.30 ERA in 65 relief appearances with 64 strikeouts and 17 walks in 62 2/3 innings for Detroit and Atlanta, which acquired him at the July 31 trade deadline. He had a 4.01 ERA in 27 games for the Braves and allowed a tying eighth-inning single to Yadier Molina in Game 4 of the NL Division Series against St. Louis, which rallied to win in 10 innings. The Cardinals won Game 5, then were swept by Washington in the NL Championship Series.
Greene is eligible for free agency after this season.