The Los Angeles Lakers star, playing in his 20th season in the NBA, passed Abdul-Jabbar's longstanding total of 38,387 points after nailing a 21-foot shot late in the third quarter against the Oklahoma City Thunder.
James flung his arms aloft in relief as the Crypto.com Arena erupted in wild celebration at his new record of 38,388 points.
Abdul-Jabbar, sitting courtside, was among the first to congratulate James as play was interrupted to salute an iconic moment in NBA history.
"To be able to be in the presence of a legend and great as Kareem it means so much to me," James told the crowd before thanking family, friends and fans.
"Everybody that's ever been part of this run with me these last 20 years, I just want to say I thank you so much because I wouldn't be me without all your help, all your passion and all your sacrifices to help me get to this point."
James signed off his on-court address with an F-bomb, seemingly lost for words after one of the signature moments of his glittering career.
James, who eventually finished the game with 38 points on the night for a career haul of 38,390, said afterwards he expected to continue playing for at least two more seasons.
"I know I can play a couple more years -- it's all about my mind," James said. "If my mind is still into it, if I'm still motivated to go out and try to compete for championships, I feel like I can still do that."
- Chasing history -
After a dazzling season that has seen him average 30 points per game in a struggling Lakers outfit, James went into Tuesday's clash with Oklahoma City needing 36 points to surpass Abdul-Jabbar.
The 38-year-old took his time before surging towards his magic number, missing his first two attempts before finally nailing a three-pointer midway through the first quarter to get off the mark.
The four-time NBA champion would go on to score eight points in the opening quarter, leaving him 28 short as the second quarter got under way.
James upped the pace in the second quarter with 12 quick points before being subbed off with 5:34 left in the half, 16 points away from the record by half-time.
A pair of back-to-back three-pointers midway through the third quarter left him just eight points away from the record, with 28 on the night, before a driving layup put him within six.
Two more layups left him two points away before he duly converted his long-range effort to seal the record.
James had been at pains to dampen anticipation surrounding his record chase this season, insisting that his priority remained helping the Lakers become a competitive outfit once more.
However, in the build up to Tuesday he was more expansive when discussing the record, saying beating Abdul-Jabbar's mark was comparable to breaking baseball's all-time home run record.
- 'Untouchable' record -
"I think it's one of the greatest records in sports in general," James said.
"I think it's up there with the home run record in baseball. It's one of those records that you just don't ever see or think that would be broken."
Many in the NBA agreed, believing that Abdul-Jabbar's record was untouchable.
"I think most of us back then thought that record would never be broken," Golden State coach Steve Kerr said of Abdul-Jabbar's record last weekend.
"So to see LeBron do it over 20 years is pretty remarkable and a testament to not only his ability but his durability.
"He's just a machine. He's healthy and a physical force night after night."
Tyronn Lue, James's former coach at the Cleveland Cavaliers, believes the scoring record is the crowning achievement of his glittering career.
"This has to be No. 1, seeing how long Kareem has held this record (since 1984). I know LeBron has his championships and MVPs. But to be the all-time leading scorer in NBA history, considering all the great players that have come through this game? That's a big-time accomplishment," Lue told NBA.com.
James, meanwhile, declined to be drawn on whether his scoring record meant he should now be considered the greatest basketball player in history.
"I'll let everybody else decide who that is," he told Lakers great Shaquille O'Neal on TNT television. "But it's great barber shop talk."