The watch, which had remained in the couple’s family, was sold at Henry Aldridge & Son Auctioneers in Devizes, Wiltshire.
The £1.78m for the item is the highest amount ever paid for Titanic memorabilia, according to the company.
A letter written by Mrs Straus on Titanic stationery and posted while onboard the ship fetched £100,000.
The previous record was set last year when another gold pocket watch presented to the captain of a boat that rescued over 700 passengers from the liner sold for £1.56m.