Droga5, which was founded in 2006 by David Droga, has become one of the best-known independent ad agencies in the United States. (The “5” was appended because Mr. Droga, 50, grew up as the youngest of five brothers.) Droga5 last reported annual revenue for 2017, when it exceeded $200 million.

Some of its notable campaigns include Under Armour’s with the dancer Misty Copeland; Anna Kendrick’s almost-Super Bowl commercial for Newcastle Brown Ale, a digital campaign in which the beer company imagined the “mega-huge football” spot it would have made if it could have afforded one; and this year’s “Game of Thrones” surprise Super Bowl ad with Bud Light. Droga5 is also responsible for The New York Times’s ad campaign featuring the motto “The Truth Is Hard.”

Being subsumed into a larger consulting firm represents a sharp turn. Other prominent independent agencies have steadfastly maintained their autonomy. In 2017, Wieden & Kennedy in Portland, Ore., which is best known for its work with Nike, backed a new agency in Austin, Tex., on the condition that it would remain independent. Colleen DeCourcy, Wieden & Kennedy’s co-president, said at the time, “Our whole abhorrence of controlling interest in anything is that you lose the independence to put the work first.”

Mr. Whipple pushed back at the notion that consultants did not understand creativity the way that traditional agencies did, saying that the cultures of Accenture Interactive and Droga5 were more similar than people might expect.

“Accenture Interactive has its own culture that is really in no way consulting-like, but I will say if it were to have elements of that, I think that’s a good thing,” he said. Its offices aren’t full of people in suits and ties talking about financials, he added.

Accenture Interactive’s revenue rose 30 percent, to $8.5 billion, for the year that ended Aug. 31, accounting for about a fifth of Accenture’s overall revenue. The unit, established in 2009, has acquired dozens of firms in recent years, but Droga5 is its biggest purchase and is expected to give Accenture Interactive new clout in North America.

Mr. Droga, who will remain the agency’s creative chairman, said that while he had fielded acquisition offers before, he felt Accenture and his agency complemented each other.