A data processing system with a processor and memory includes an instruction set architecture (ISA) that provides an asynchronous memory move (AMM) store (ST) instruction. When the processor executes the AMM ST instruction, the processor performs a series of functions, which initiates an asynchronous memory move (AMM) operation. The AMM ST instruction moves data from a first memory location having a first real address to a second memory location having a second real address by: (a) performing a move of the data in virtual address space utilizing a source effective address that is memory mapped to the first memory location and a destination effective address that is memory mapped to the second memory location. When the move is completed in the virtual address space, the AMM operation performs the physical move of the data to the second memory location outside the processor core, without processor involvement.