He follows Chris Columbus - who directed the first two Potter films - and Alfonso Cuaron - who's currently working on Potter 3 - into the job.
Goblet Of Fire will start shooting next April.
Alfonso will still be working on Potter 3 - the Prisoner of Azkaban - at that time, so he was unable to take on the next movie in the series.
Warner Bros said: "We've been lucky to have worked with excellent filmmakers on the first three movies and we are looking forward to continuing that tradition as we start on this next movie with Mike."
Mike said he was "very excited" about the job.
The first two Potter films - Philosopher's Stone and The Chamber Of Secrets - broke movie records around the world.