A hybrid vehicle drive apparatus includes an engine, a transmission unit, and a differential unit. A dual-motor travel is possible by stopping the engine and driving a first rotating machine and a second rotating machine as a result of engaging a first engaging element and a second engaging element of the transmission unit. At a time of switching to a dual-motor travel, the hybrid vehicle drive apparatus executes a first control for carrying out a negative RPM control by the first rotating machine; a second control for engaging either one of a first engaging element and a second engaging element of the transmission unit; and a third control for engaging both of the first engaging element and the second engaging element of the transmission unit after the first control and the second control.