In all likelihood, the increased sales will be enough to cover the earlier weekly box office losses and, perhaps, pay a little money back to the show’s investors. (Sting is not an investor himself.) After Sting leaves, it would be something of a miracle if ticket sales remain durable. (He will resume his tour with Paul Simon on Jan. 30 in New Zealand.) Without Sting, “The Last Ship” has been grossing about $500,000 to $600,000 a week, low amounts for a show by a famous artist. It needs to gross at least $625,000 a week to break even and sustain a Broadway run.

The last time a Broadway show tried something like this, the results were mixed. The musical “American Idiot,” based on the album by Green Day, was in trouble at the box office in the fall of 2010, when Green Day’s popular frontman, Billie Joe Armstrong, joined the cast for a week in a supporting role — and then came back for two longer stretches. Predictably, “American Idiot” ticket sales exploded when Mr. Armstrong was in the cast: Green Day fans wanted to see their idol singing Green Day songs. The show went from $480,566 (for the week before Mr. Armstrong began in September 2010) to $1,092,334 for the week when he played the role of St. Jimmy. The following week, after Mr. Armstrong departed, the show dropped back to $567,731. (“American Idiot” did not turn a profit on Broadway.)

While producers often hire big-name actors to drive ticket sales, it is rare for a superstar creator to join a show midrun. Last week, “Hedwig and the Angry Inch” announced that John Cameron Mitchell, who created the character of Hedwig and wrote the show’s book, would play the title role in January and February: a move that will most likely firm up ticket sales through those two months, which are traditionally tough times, even for hits like “Hedwig.” By contrast, the musical “Spider-Man: Turn Off the Dark” had a score by Bono and the Edge of U2, but they were on tour during early performances and were criticized for not doing more to help the show.

Jeffrey Seller, the lead producer of “The Last Ship,” said that he asked Sting to perform in part in hopes of creating momentum to keep the show running into Tony Awards season in June. “Our goal is to win the Tony” for best musical, he said.

“We need a boost, we need to break through, we need some ammo,” Mr. Seller said, pointing to Sting during the interview. Sting is scheduled to make the official announcement about joining “The Last Ship” on Monday during an appearance on NBC’s “Today” show, and will also perform in the televised Macy’s Thanksgiving Day Parade.

Mr. Seller has deep experience turning slow-building shows into hits, like “Avenue Q.” In this case, he blamed himself for an early advertising campaign that emphasized shipbuilders and not the show’s love story. “I feel like I screwed up,” he said, adding that the new campaign will obviously be built around Sting.

Sting said he had no worries about preparing: “I know all the lines and lyrics after all these years,” he said with a laugh. His only concern is showing that “The Last Ship” deserves audience support for its originality.

“There’s no point in having a hit that obeys formulas,” he said. “I want to have a hit. I want it to be hugely successful. But I want it to be an original.”