The X-Men star will also perform songs from Les Miserables and other Broadway shows accompanied by a live orchestra.
The Greatest Showman has become a worldwide phenomenon with a record breaking soundtrack, despite lukewarm reviews.
The tour will include four dates in the UK in Manchester, Birmingham and London.
The Wolverine star was nominated for an Oscar for his performance as Jean Valjean in the movie version of the musical Les Miserables.
He won a Golden Globe for his performance and was also nominated for a Globe for his turn in The Greatest Showman.