The sequels, according to hollywoodreporter.com, will reunite the stars of the 2003 blockbuster - Johnny Depp, Orlando Bloom and Keira Knightley.
Director Gore Verbinski, writers Ted Elliott and Terry Rossio and producer Jerry Bruckheimer will remain at the helm.
In the new films, Skarsgard will play Bloom's long-lost father and Harris will play a gypsy queen.
"Pirates 2" is scheduled for a summer 2006 release. Shooting is to start in early March in Los Angeles and the Caribbean.