Fox replaces Disney, which bowed out in December citing "budgetary considerations and other logistics".
The second film in the series, Prince Caspian, made $420m (£295m) compared with the $745m (£523m) made by 2005's The Lion, the Witch and the Wardrobe.
The next movie is due to be released in 2010, Fox said.
The Narnia movies, which have won an Oscar for make-up, cost Disney and co-producers Walden Media an estimated $180m to $200m (£126m to £140m) to produce, and both films went on to become top DVD sellers.
No information has been released about the production costs for the new film which sees the Pevensie children take another member of the family - cousin Eustace - into Narnia.