Borrego agreed to a four-year deal, with the Hornets holding a team option on the fourth year of the contract, league sources said.
He is is believed to be the first Hispanic-American to be a full-time NBA head coach. Kaleb Canales, who is Mexican-American, served as interim coach of the Portland Trail Blazers for the final 23 games of the 2011-12 season.
Borrego, 41, has already started working to build his coaching staff with the Hornets, after beginning work on finalizing the contract Tuesday, league sources said.
Borrego met with Hornets owner Michael Jordan over the weekend, after advancing to the final group of interviews along with Celtics assistant Jay Larranaga.
The Hornets were sold on Borrego's strong credentials as one of Gregg Popovich's longtime assistants, including his abilities in player development, devising game plans on both the offensive and defensive ends, and building relationships with players.
He will be challenged with a veteran team high in payroll and low in salary-cap flexibility and upside. Charlotte's best player, All-Star guard Kemba Walker, will be entering the final year of his contract. Walker had a close relationship with former coach Steve Clifford.
Borrego is one of the most well-regarded assistants in the league, and his career has included two tours on Popovich's coaching staff. He turned down the University of New Mexico in his home state last year, choosing to continue his pursuit of an NBA head-coaching job.
Borrego made a strong impression on Mitch Kupchak, the Hornets' new president of basketball operations and general manager, during his interview. Kupchak became more intrigued once he started to canvass NBA executives, coaches and players who have worked with Borrego.
Borrego interviewed for the New York and Phoenix openings this spring, and was set to interview with the Milwaukee Bucks until Charlotte's offer, league sources said. Borrego interviewed for the Houston Rockets and Memphis Grizzlies jobs in 2016, becoming a finalist for both positions.
The Hornets had met with coaches, including new Knicks coach David Fizdale, San Antonio assistants Ettore Messina and Ime Udoka, and Portland assistant David Vanterpool.
Borrego has been an NBA assistant with the Spurs, Pelicans and Magic since 2003. He was 10-20 as interim coach of the Orlando Magic to finish the 2014-15 season.