A data processing system has a processor, a memory, and an instruction set architecture (ISA) that includes: an asynchronous memory mover (AMM) store (ST) instruction that initiates an asynchronous memory move operation that moves data from a first memory location having a first real address to a second memory location having a second real address by: (a) first performing a move of the data in virtual address space utilizing a source effective address a destination effective address; and (b) when the move is completed, completing a physical move of the data to the second memory location, independent of the processor. The ISA further provides an AMM terminate ST instruction for stopping an ongoing AMM operation before completion of the AMM operation, and a LD CMP instruction for checking a status of an AMM operation.