The drama, which will air on ITV in the UK and ABC in the US, features a cast including Linus Roache, Geraldine Somerville and Timothy West.
It is expected to focus on the lives of the passengers and crew on the famous ship and will feature stories of romance and mystery. Both fictional and historical characters will be included in the drama.
The show is being filmed in Budapest on a two-tier set which includes a promenade deck, boat deck, four working lifeboats, two collapsible lifeboats, the ship's bridge, corridors and several rooms.
The team behind the drama has also built the biggest indoor tank in mainland Europe for the scenes set in water.
The project's director Jon Jones said: "It's an incredible, evocative playing space. We have built a huge section of the ship that is jam-packed with a warren of rooms arranged to allow us a sense that we have the run of the ship. Once you enter the studio, it is like boarding the ship - you get a real sense of the space. We want to get to grips with how it really was to be confined in a tiny cabin in steerage - or effortlessly ensconced in a First Class stateroom."
Fellowes has previously admitted that he is "terrified" about producing a new version of the Titanic story after James Cameron's famous 1997 movie.
Titanic will air in April 2012 to mark the centenary of the ship's sinking.