Financial terms and length of contract were not disclosed.
Miller, who was amnestied by the Miami Heat last week, also reportedly drew interest from the Oklahoma City Thunder, Houston Rockets and Denver Nuggets.
The Heat saved as much as $17 million on luxury-tax payments next season by waiving Miller, but still owe him $12.8 million in salary over the next two seasons.
Miller, 33, averaged 4.8 points in 59 games last season and spent six seasons with the Grizzlies from 2002-08.
Miller has battled numerous injuries over the years, but came through in a big way in the Finals against the San Antonio Spurs. He hit 11 of 18 shots from 3-point range in the series.
"I'm excited about the next spot. I'm re-energized. I really am. I'm just feeling healthy. I'm ready to play. I started to get back in there again last week and I can't wait to play again next year," Miller said on Tuesday.