Phoenix also assigned defenseman Chris Summers to the Portland Pirates of the AHL.
O'Reilly had one assist in five games with Nashville this season. The 25-year-old appeared in 38 games with the Predators last season, scoring career highs of six goals and 12 assists.
O'Reilly has 11 goals and 24 assists in 85 career NHL games, all with the Predators.
The trade is conditional upon O'Reilly passing a physical.