Some donned period costume, including furs and feathered hats for women and suits and bowler hats for men, to board the MS Balmoral at Southampton on the southern English coast.
Passengers lined the decks and waved as the ship set sail almost 100 years after the Titanic set off on her maiden voyage from Southampton to New York.
The Titanic was considered unsinkable but foundered in frigid Atlantic waters off Newfoundland on April 15, 1912, after striking an iceberg.
Around 700 people were rescued but there were too few lifeboats to save the rest.
The world's most famous maritime disaster has fascinated people ever since, explaining why passengers from 28 countries were prepared to pay up to 8,000 pounds ($13,000) each to be a passenger on the memorial cruise organized by a British travel firm.
The Balmoral will follow in the wake of the Titanic, sailing near Cherbourg in France and then calling at Cobh inIreland before arriving at the spot where the Titanic went down. There, on April 15, a memorial service will be held on board to mark the centenary of the disaster.
Passenger Jane Allen, whose great-uncle died on his honeymoon trip on the Titanic while her great-aunt survived, said she did not think it was "ghoulish or macabre" to go on the voyage.
"I've been to World War One and Two cemeteries in various places across the world and I think it is always important to remember. The people here in the Titanic died in very different circumstances but it was still quite unbelievable what happened that night," she told theBBC.
Organizers said 1,309 paying passengers booked on the memorial voyage.
While the Balmoral is a modern ship, the 12-night memorial cruise will try to recreate the atmosphere of the time with dishes and music from the era, while experts will give lectures about the Titanic.
A 3D version of ames Cameron's 1997 blockbuster movie "Titanic" has just been released to coincide with the centenary of the sinking of the luxury liner.
The first Titanic and zombie mashup book was released this week, by Amazon.com, called "Titanic of The Dead: How I Survived the Titanic Zombie Apocalypse" by Stephen Dymarcik [Paperback] and [Kindle]. Purportedly a DECLASSIFIED first hand account of the Titanic from 1912.
A $150 million Titanic centre telling the story of the doomed liner has just opened in Belfast, Northern Ireland, beside the slipway from which the liner was launched by the Harland and Wolff shipyard a century ago.
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