Paul can't sign his new contract until July 10 but could agree to terms as of 12:01 a.m. ET.
"I'm in. ClipperNation," Paul tweeted.
Paul always intended to stay with the Clippers, sources said, and that sentiment was only strengthened when the team tabbed Doc Rivers as head coach and senior vice president of basketball operations earlier this week.
Paul will become the second high-profile player to sign a long-term extension with the Clippers in the past two seasons. Blake Griffin signed a five-year, $95 million extension last summer.
Paul, a two-time Olympic gold medalist who led the Clippers to their first Pacific Division title last season, has helped turn around the Clippers franchise in two seasons since coming in a trade from New Orleans.
The Clippers have made the playoffs in both of his seasons, advancing to the second round in 2012, and went 56-26 last season for the best record in their history.
Paul averaged 16.9 points, 9.7 assists and an NBA-best 2.4 steals per game. He was the Western Conference player of the month in December, when the Clippers went 16-0.
Paul spent his first six seasons with New Orleans before he was dealt to the Clippers, shortly after the NBA, then serving as owners of the then-Hornets, stopped a trade that would have sent him instead to the Lakers.
Paul missed 12 games last season with a bruised right kneecap and played a career-low 33.4 minutes per game, and still was second in the league in assists and first in assist-to-turnover ratio. He was MVP of the All-Star Game and finished fourth in voting for the regular-season award.
The Wake Forest product is also one of the league's most popular players, serving as an executive on the NBA players' association.
Information from ESPN The Magazine's Chris Broussard and The Associated Press was used in this report.