Chapelcross near Annan was on a shortlist of five potential locations.
Capenhurst in Cheshire has been selected to store the nuclear components, with Aldermaston in Berkshire as a "fall back" option.
The Scottish site was ruled out along with Sellafield in West Cumbria and Burghfield in Berkshire following public consultation.
Chapelcross was home to Scotland's first commercial nuclear station, which was built on old airfield in Dumfriesshire. The site ceased generation in 2004.
The nuclear components are from 18 redundant submarines and nine still in service.
The redundant Royal Navy submarines are currently stored afloat at Devonport in Plymouth and Rosyth in Fife, but cannot be dismantled until the reactor components have been removed.
The radioactive parts will be stored until after 2040, when the UK's Geological Disposal Facility, for the permanent disposal of spent fuel and nuclear waste, is planned to come into operation.
Defence Minister Philip Dunne said: "When submarines in the Royal Navy fleet reach the end of their lives, we need to dispose of them in a way that is safe, secure and environmentally sound.
"We have worked closely with the local communities around potential sites to listen carefully to their views, and the opinions and feedback we received has played an important part in formulating our final decision.
"With Capenhurst as our recommended site, we know that the radioactive waste from our decommissioned submarines will be dealt with properly and responsibly."
The Ministry of Defence has ruled out a Scottish site as a possible location to store waste from nuclear submarines.