It is being showcased as part of the Franklin Outreach Project, a joint initiative between Parks Canada and the Toronto museum, that aims to share the story of the expedition with Canadians.
"The bell that was recovered from the ship requires extensive conservation and so the creation of a full-size 3D replica — the only one in the world — seems to us to be a great way to launch this project," said Janet Carding, the museum's director and CEO.
The two ships of the Franklin expedition and their crews, 129 members in all, disappeared during the 1845 quest for the Northwest Passage.
The Erebus, the vessel on which Sir John Franklin himself sailed, was discovered in September. So far, the location of the other ship, HMS Terror, remains a mystery.
The Franklin Outreach Project will include pop-up displays, lectures and exhibitions incorporating modern technology and Inuit traditional knowledge to bring the Franklin story to life.
"I am particularly proud that this project will have a focus on traditional knowledge," said Leona Aglukkaq, the minister responsible for Parks Canada.
"It will help Canadians learn how Inuit traditional knowledge and the testimony of Inuit elders led us to the right search area."
Since 2008, Parks Canada has led six major searches for the lost ships, which long ago captured the Victorian imagination and gave rise to many searches throughout the 19th century for Franklin and his crew.
The mystery of exactly what happened to Franklin and his men has never been solved.
The Parks Canada-ROM partnership will last three years, during which the exhibit will travel to seven other museums countrywide.