Swede Malkolm Johnson, 33, who failed to get on a lifeboat after the ship hit an iceberg on its maiden voyage in 1912, had dived into the Atlantic wearing a life jacket.
But he did not survive due to the blistering cold, and his body and possessions were later recovered, with his watch stopped at 1.37am.
His family are selling off the heirlooms, which have never been seen before, and the timepiece is expected to fetch 8,500 pounds.
Johnson's third-class table ticket, a ring and other items are also up for auction on May 26.
"The watch may mean he was aboard Titanic until she vanished under the surface," the Sun quoted Erik Ingare, of Bukowskis auctioneers in Stockholm, as saying.