Clifford's contract is for three years, $6 million, the source said, with a team option for the third year.
Yahoo! Sports earlier reported that Clifford and the Bobcats had agreed in principle.
The Bobcats fired coach Mike Dunlap in April after one season with the team.
Clifford came to the Lakers from Orlando last season, in part because of his close relationship with Dwight Howard. He was retained by Mike D'Antoni after the season, but the Lakers gave him permission to interview elsewhere.
Clifford also spent four seasons as an assistant with the Rockets under Jeff Van Gundy and three with the Knicks.
Jeff Van Gundy, now an NBA broadcaster, said he's known Clifford since they coached together at the Jim Boeheim camp in 1985 in Syracuse, N.Y., and called him "a person with impeccable integrity."
He also thinks he's going to be a pretty good NBA head coach because of the relationships he builds with players and fellow coaches.
"He's a brilliant basketball coach who relates to all kinds of people well and I think he will do an absolutely fantastic job with the talent at hand," Jeff Van Gundy said. "I'm so happy for one of the good guys in the league to get this opportunity."
The Lakers have now lost the two assistants who are closest to Howard, who becomes a free agent on July 1. Assistant coach Chuck Person, who has close ties to both Howard and Kobe Bryant, was not retained by D'Antoni after the season.
Clifford also interviewed for the Milwaukee Bucks job.
The Bobcats went 21-61 under Dunlap, finishing with the second-worst record in the NBA, ahead of only the Orlando Magic. Charlotte won just seven games in the lockout-shortened 2011-12 season, but tripling last season's victory total and a three-game winning streak to close the season weren't enough to save Dunlap's job.
Dunlap struggled at times with game management, transitioning from the college game to the NBA and handling professional athletes, often benching veteran players for weeks at a time after they'd irritated him in some way.
Dunlap replaced Paul Silas, who was fired after the Bobcats went 7-59 in 2011-12, the worst winning percentage in NBA history at .106.
Along with Clifford, the Bobcats interviewed at least five other known candidates for the position.
They spoke early on in the process to former Los Angeles Clippers and Phoenix Suns coach Alvin Gentry, Suns assistant Elston Turner, Cleveland Cavaliers assistant Nate Tibbetts and Houston Rockets assistant Kelvin Sampson.
The Bobcats again considered former Lakers assistant Quin Snyder, now a head coach of a professional team in Russia. Snyder and Jerry Sloan were among the three finalists for the job last year that was given to Dunlap.
Information from The Associated Press was used in this report.