Butler reached a buyout agreement with the Milwaukee Bucks and was waived on Thursday. The Heat also were interested in acquiring Butler, who played his first two NBA seasons with Miami and remains close with Heat star Dwyane Wade.
The Thunder might be able to give Butler more playing time as a backup to Kevin Durant. Oklahoma City, which is without center Kendrick Perkins for up to six weeks, could use more smaller lineups the rest of the season, which may open up chances for Butler.
The 34-year-old Butler averaged 11.0 points and 4.6 rebounds in 34 games for the Bucks. He has battled a high ankle sprain that's cost him time recently and is shooting a career-low 39 percent. But he scored 17 or more points four times in his past 10 games.