Bruce Springsteen is recording his Broadway show and will release it as a Netflix special on Dec. 15, the day of the production’s final onstage performance.

He invited a private audience for two extra performances this week — one Tuesday and one Wednesday — while cameras recorded the event for the special.

“Springsteen on Broadway,” which has been running at the 948-seat Walter Kerr Theater since October, is a reflective two-hour program in which Mr. Springsteen intersperses stripped-down versions of some of his most popular songs with stories about his life adapted from his memoir, “Born to Run.” He performs the show mostly alone — accompanying himself on piano, guitar and harmonica — but is also joined for a few songs by his wife, Patti Scialfa.

The show has been an enormous financial success, with an average price of about $510 per ticket (that’s the face value — some people pay more to purchase from resellers). As of Sunday, the show had grossed $76 million and had been seen by a total audience of 151,549 people. Mr. Springsteen generally does four or five shows a week — fewer than the usual eight for most Broadway productions — and has taken several weeks off; as of Sunday he had performed the show 160 times.