“I did get more than I bargained for, but in a great way,” Melanie Batchelor, vice president for global spirits, said by phone from Campari offices in Italy. “Personally, I have been completely overwhelmed with his level of commitment.”

The celebrity endorsement has been part of Madison Avenue’s playbook since at least the 1940s, when film stars were paid to promote cigarettes. But only in the last decade have Hollywood A-listers been willing to let a consumer brand define them to the same degree as a movie role. Mr. McConaughey, for instance, is now just as famous (or more) for his Lincoln car commercials as for “Dallas Buyer’s Club,” the film that won him the 2014 Academy Award for best actor.

Yet there are downsides to ad work. Mr. McConaughey’s eccentric Lincoln ads have been mocked by “Saturday Night Live” and “The Ellen DeGeneres Show.” (“I actually think they’re cool little pieces of art,” Mr. McConaughey said of the spots. “They’ve been good for Lincoln and good for me.”)

Stars invariably overlook the risks because the advertising partnerships, unlike most movie roles these days, can bring enormous paychecks: Deals like the one Mr. McConaughey made with Wild Turkey are typically worth tens of millions of dollars, talent agents say.

“I’ve always been interested in the art of the sell,” Mr. McConaughey said, noting that he interned as a college student at an Austin, Tex., advertising agency, where he worked on a “Don’t Mess With Texas” commercial.

After being hurt by distillery underinvestment in the 1980s and the vodka boom of the 1990s, bourbon has experienced blistering growth over the last decade, as the “Mad Men” and classic cocktail crazes helped consumers rediscover brands like Pappy Van Winkle and Old Crow. For the fiscal first quarter, which ended in March, domestic sales of Wild Turkey increased 7.6 percent from the same period a year earlier.

But Campari wants Mr. McConaughey to supercharge Wild Turkey sales both in the United States and overseas. “Older, particularly Southern, gentlemen have always loved the brand, but we need to close the gap between our perceived quality and our actual quality,” Ms. Batchelor said. In other words, many people see Wild Turkey as a downscale choice, and Campari wants to change that.