Prime Minister Stephen Harper is expected to announce the news today in the House of Commons.
Two ships, HMS Erebus and HMS Terror, were part of Sir John Franklin's doomed expedition in 1845 to find the Northwest Passage.
The ships disappeared after they became locked in ice in 1846 and were missing for more than a century and a half until last month's discovery by a group of public-private searchers led by Parks Canada. It was not known until now which of the two ships had been found.
The Erebus is believed to be the ship that Sir John Franklin was on when he died. The wreck of the Terror has not yet been found.
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