The sale, which closed in late June, represents the highest price ever paid for a Las Vegas home, according to the Greater Las Vegas Association of Realtors.

Ivan Sher of Berkshire Hathaway HomeServices Nevada Properties represented both Mr. Copperfield and the seller, health-care executive Kevin Hooks.

Mr. Hooks bought the land for $2.575 million in 2005 and built the house, completing it around 2011. The contemporary steel-and-concrete home was not officially on the market. Mr. Copperfield and his fiancee, Chloe Gosselin, “had been looking for years,” Mr. Sher said in an email. “Nothing really spoke to them,” he said, until they came across this property.

The eight-bedroom house is located in a gated community in the Summerlin neighborhood. The four-story main house measures about 19,425 square feet. Two elevators run from the roof deck to a subterranean garage, which has a detailing room. The house also includes a nightclub with a bar and dance floor, a gym with two adjacent massage rooms, a wine cellar, and a movie theater.

The roughly 1.58-acre property also includes two guest houses, a golf simulator and an infinity swimming pool.

Mr. Copperfield, 59, is known for illusions such as “vanishing” the Statue of Liberty and escaping from Alcatraz prison. He is currently in residence in Las Vegas at the MGM Grand Hotel & Casino David Copperfield Theater. His other homes include a Manhattan penthouse and an archipelago of 11 islands in the Bahamas.

Mr. Hooks could not be reached for comment.