It is unclear what the Marlins are receiving in return, although right-handed pitching prospect Sandy Alcantara reportedly is included in the deal, per reports.
The trade, which reportedly is in place pending a physical, comes on the heels of two other big-name departures by the new Marlins regime, led by co-owner and CEO Derek Jeter.
Miami traded reigning National League MVP Giancarlo Stanton to the New York Yankees on Monday in exchange for second baseman Starlin Castro, minor league right-hander Jorge Guzman and minor league infielder Jose Devers.
Ozuna recorded career highs in batting average (.312), home runs (37) and RBIs (124) last season. The 27-year-old owns a career .277 average with 96 home runs and 361 RBIs in five years with the Marlins.
Alcantara, 22, debuted in September and recorded a 4.32 ERA in eight relief appearances with the Cardinals.