Sources told ESPN.com that the Utah Jazz center, after a two-day visit with the Bobcats, has verbally agreed to a three-year contract with Charlotte worth an estimated $41 million.
The deal contains a player option in Jefferson's contract after the second year, sources said.
Jefferson can't formally sign the contract until July 10, the first day teams and free agents can make deals official after the league's annual moratorium is lifted.
The Bobcats will release Tyrus Thomas this month via the one-time amnesty clause to create the needed salary-cap space to sign Jefferson, according to TNT. Jefferson instantly becomes the biggest free-agent signing of Michael Jordan's time in Charlotte.
Jefferson, 28, gives the Bobcats a much-needed scoring threat in the low post, where they struggled last season. He should also help on the boards, where the Bobcats were repeatedly outrebounded the past two seasons.
The 6-foot-10, 289-pound Jefferson has averaged 18.8 points and 10 rebounds per game over the past seven seasons. Last season, his third with the Jazz, he averaged 17.8 points, 9.2 rebounds and 2.1 assists per game.
The Boston Celtics selected Jefferson out of high school in Mississippi with the No. 15 pick in the 2004 draft. During a nine-year NBA career, Jefferson also played three seasons for the Minnesota Timberwolves.
He has career averages of 16.4 points, 9.0 rebounds and 1.5 assists a game.
Jefferson was among four high-profile free agents who played last season with the Jazz, along with Paul Millsap, Mo Williams and Randy Foye. Utah went 43-39 and missed the playoffs for the second time in three years.
Acquired by the Jazz in a July 2010 trade, Jefferson earned $15 million last season and led the team in scoring and rebounding. After the 2012-13 season ended, Jefferson told reporters he believed he improved his overall game while in Utah.
"I have showed I'm not just the black hole reputation I had years ago," Jefferson said in April, referring to claims he never passed the ball out of the post. "I showed people that I can do other things."
In April, Jazz coach Tyrone Corbin praised Jefferson for his contributions in Utah.
"He's done a great job, coming in, being known as an offensive player, getting numbers," Corbin said. "And he's gotten numbers here, but they've helped us win a lot of games. He's been healthy. He's always ready and willing to play and likes to be on the floor, and I think he's been a great guy with this team of guys."
Jefferson, who was given credit for helping develop young players Derrick Favors and Enes Kanter, said it was emotional to say goodbye to his Jazz teammates at the abrupt end of the season. The Jazz finished just out of the playoffs in ninth place in the Western Conference.
"There's no way in the world every one of these guys will be here next year, all together," Jefferson said.
Jefferson becomes the best low-post scoring threat the Bobcats have had in nine years in the NBA.
The Bobcats are 28-120 over the past two seasons, and their most high-profile player is second-year point guard Kemba Walker.
Information from The Associated Press was used in this report.