The musical premiered Jan. 25 at San Diego's Old Globe Theatre and was extended twice through March 19, Playbill.com reported.
Tharp directs the show and also choreographed Dylan's music, which he calls "the best presentation of my songs I have ever seen or heard on any stage."
"Twyla's artistry knocks me out," Dylan said.
The play is set in a traveling circus run by Capt. A. Rab whose entourage hasn't moved for some time. His son, Coyote, dreams of life outside the circus, but must decide whether to escape or to make change within the troupe.
The show is billed as "a fresh exploration of the timeless tale of a young man's coming of age."
Original stars Michael Arden (Coyote), and Thom Sesma are joined by "Movin' Out" veteran John Selya and new addition Caren Lyn Manuel for the Broadway run starting Oct. 26.