The Titanic Memorial Cruise arrived at the town of Cobh, on Ireland's southern coast, about two hours later than scheduled due to the bad weather, Rachel O'Reilly said.
The vessel, called the MS Balmoral, set sail from Southampton in southern England on Sunday for the 12-night cruise.
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Cobh, once known as Queenstown, was the Titanic's last port of call before it set out across the Atlantic in April 1912. As the Balmoral pulled into the town's port on Monday, it was welcomed by thousands of cheering well-wishers.
The ship, which carries 1,309 passengers - including relatives of some of the more than 1,500 Titanic passengers who died - will leave Cobh for the North Atlantic site where the ship hit an iceberg and sank, O'Reilly said.
The cruise seeks to recreate the experience onboard the Titanic - minus the disaster. Many passengers are dressed in period costumes for the journey, as are crew members and stewards.
Passengers will also eat meals from the Titanic's menu, while a live band plays music of the era.
Two special memorial services will take place over the weekend: The first close to midnight April 14, when the Titanic hit the iceberg, and the second on early April 15, when the ship sank.
The Balmoral is operated by Fred Olsen Cruise Lines, whose parent company, Harland and Wolff, built the Titanic in Belfast.
The memorial cruise is among an abundance of commemorations and memorials to the reputedly unsinkable ship that have sprung up to coincide with the 100th anniversary of the Titanic's doomed voyage.
