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.
Jackman plays circus impresario PT Barnum in the musical film which has songs by Tony and Oscar-winning songwriting duo Benj Pasek and Justin Paul.
Critics weren't keen on the film but its popularity spread by word of mouth, with fans returning for repeat viewings and attending special singalong screenings.
The soundtrack has also broken records around the world. It was number one in the UK album chart for 11 weeks in a row equalling Adele's record for her album 21.
It was number one for 21 weeks in total, overtaking Saturday Night Fever to become the longest-running number one soundtrack since the 1960s.
The Man, the Music, the Show is Jackman's first world tour.