A manned flight to lunar orbit is planned for four years after that, the agency said.
The Boeing upper stage is "the only means available to support the immediate in-space propulsion needs" for the excursions, NASA said in a statement.
An internal study of in-space propulsion systems available in the United States, Europe and Japan determined the Delta IV upper stage "is the only known in-space stage requiring relatively minor modifications" to meet mission requirements as well as the launch schedule, NASA said.
The Delta IV second stage is powered by a single Pratt & Whitney RL-10B2 engine fueled by liquid hydrogen and liquid oxygen.
Both Orion missions will be launched from complex 39B at Kennedy Space Center on early versions of NASA's new heavy-lift Space Launch System, Florida Today reported.