The 1,309 passengers of the MS Balmoral will attend a memorial service for the people who died in the tragedy. About 50 people on board have a direct family connection to the sinking.
The Balmoral left Southampton on Sunday for a 12-night cruise to commemorate the centenary of the sinking of the liner that hit an iceberg on its maiden voyage.
A spokeswoman for the cruise said when the clocks reach 11.40pm on the ship - the time the Titanic hit the iceberg - the captain will make an announcement and the names of those who died will be read out. One hour and twenty minutes later, a Christian memorial service will be held, a spokesman for the cruise said.
Patricia Watts, 81, a retired teacher from Bristol who is travelling with her husband David, 80, will be remembering her grandfather, George MacKie, 34, from Southampton, who was a second class steward on board the Titanic.
She said: "When we get to the wreck site there will be some sadness, but I think also some sense of release.
"I shall feel a sense of accomplishment that I have achieved what I set out to do. I think the service will be a very memorable occasion, slightly sad, but also for a lot of people it will be the event of the cruise"