Radcliffe, 24, will arrive first, in April, for a limited engagement of Irish playwright Martin McDonagh's 1930's period black comedy The Cripple of Inishmaan – about a young man with basically nothing who aims to get cast in a movie when a Hollywood crew comes to his coastal village.
The play will open April 20, four days before the cut-off for the Tony Awards deadline, notes The New York Times, and run through July 20.
The Harry Potter star's last foray on the Great White Way was a 2011 revival of the classic musical How to Succeed in Business Without Really Trying. Though a hit at the box office thanks to his star power, Radcliffe was snubbed when the Tony nominations were announced.
Critically, he scored better in a 2008 revival of the drama Equus, which earned him a Drama Desk nomination. The production was also notable for his nude scenes.
Jackman, 45, who frequently sheds his shirt on stage – and is "one of the theater world's most lucrative draws," writes The Times's Patrick Healy – will return next season in the Jez Butterworth play The River.
In its review when the show played London's Royal Court Theatre in 2012, the Telegraph likened the drama, which has a mystery at its core, to "a subtly crafted piece of chamber music. It is teasing, haunting and hushed, with just three speaking roles for unnamed characters."
The announcement of Jackman's return almost compensates for the recent disappointment of his pulling out of the upcoming musical Houdini, about the iconic escape artist.