The Ryou-Un Maru was first spotted off the coast of Canadian British Columbia on 23 March.
The vessel was moving at about 1km/h in a maritime transport corridor that separates US and Canadian waters.
It was adrift about 195 miles from Sitka, Alaska, when it was sunk, officials said.
Chief Petty Officer Kip Wadlow told AP news agency that a cutter was used to fire cannon at the abandoned ship, which burst into flames and took on water.
After a few hours, larger ammunition was used to complete the job, he said.
A Hercules C-130 air crew was ready to participate in the operation, broadcasting to mariners and air traffic to alert them and help clear the surrounding area before the demolition of the ship began.
CPO Wadlow said it would be too expensive to try to salvage the ship, and too dangerous to put anyone on board.