The sequel to Pirates of the Caribbean took £2.3m at the UK box office on its first day of release, Disney's biggest ever first day opening.
Depp will reprise his role in a third Pirates film next year
Advance ticket sales for Pirates of the Caribbean: Dead Man's Chest, starring Johnny Depp and Keira Knightley, topped the £1m mark.
The follow-up to the 2003 original is also expected to fare well in the US.
Some film analysts are predicting the film will make over $100m (£54m) in its first three days.
"It just has everything going for it to give it one of those openings that everyone is going to talk about," said Paul Dergarabedian, president of entertainment research company Exhibitor Relations.
The movie will open in 4,133 venues across the US, making it the third-widest released film after Spider-Man 2 and Shrek 2.
The first film, whose full title is Pirates of the Caribbean: The Curse of the Black Pearl, made $654m (£353m).
A third movie is in the pipeline, starring rocker Keith Richards in a cameo role as the father of Captain Jack Sparrow, played by Johnny Depp.
Some observers have drawn comparisons between Depp's performance as the pirate and the 62-year-old Rolling Stones guitarist.