Criss, who made his Broadway debut Jan. 3 with the production, will conclude his limited three-week engagement Jan. 22. Jonas will step in following the "Glee" star's departure and join Emmy Award winner Beau Bridges for a run through July 1.
Jonas, who was most recently seen on stage as Link Larkin in the Hollywood Bowl production of Hairspray, has also been seen on Broadway in Annie Get Your Gun, Beauty and the Beast and Les Miserables.
Here's how producers describe How to Succeed: "With the aid of a trusty self-help book 'How to Succeed in Business Without Really Trying', wily window washer J. Pierrepont Finch (Jonas) enjoys a riotous rise up the corporate ladder. Can he get the promotion, the corner office and the girl, or will he learn that balancing business and pleasure can be precarious—but hilarious—and oh, so much fun?"
To check out the interview with Jonas, look below:
