Playbill.com previously reported that Jackman was in the recording studio with Pasek and Paul, though the Christmas Story songwriters' involvement had never been officially announced until now.
"The Greatest Showman on Earth" will also feature song contributions by Bonnie McKee, Brian Lapin and "Scissor Sisters" front man Jake Shears.
"The Greatest Showman on Earth" will focus on P.T. Barnum's life in showbusiness and the creation of the three-ring circus.
Filming is expected to begin this summer in New York City.
Jackman is currently back on Broadway in the new drama The River.