The Titanic Memorial Cruise is carrying 1,309 passengers, the same number as were on the White Star ship, and departed from Southampton docks in southern England.
Many turned up to board the MS Balmoral in period Edwardian costumes, with some as first class passengers, others as steerage travellers and some as crew.
As part of the 12-night voyage, the cruise will also stop at the location in the Atlantic Ocean where the original ship hit an iceberg and sank on April 15, 1912, and those on board will hold a memorial service.
“It is still quite unbelievable what happened that night,” said Jane Allen, who was travelling on the memorial cruise with her husband Frank.
She said her great aunt and uncle left on the Titanic on their honeymoon. The aunt survived aboard one of the lifeboats, but her uncle stayed on board and was among the more than 1,500 people who died.
Around 50 of those on board were related to Titanic victims, organisers said.
Passenger Graham Free, 37, was dressed as a Edwardian gentleman but said he did not think the cruise was exploiting the tragedy.
“I have been a fan of the Titanic since I was nine years old and this cruise is the closest you are going to get to it,” he said.
Organisers are trying to recreate the experience of travelling on the Titanic – albeit safely this time – with food from the original menus and a band from Belgium to play period music.
The band is in honour of the musicians who played on the Titanic as it sank beneath the waves with the loss of 1,514 lives.
People from 28 different countries booked places on the voyage, which cost between £2,799 and £5,995 (B137,300 and B294,000) per person.