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 also paid tribute to NBA commissioner Adam Silver and his predecessor, the late David Stern.
"Thank you guys so much for allowing me to be a part of something I've always dreamed about, and I would never ever in a million years have dreamt this even better than what it is tonight," James added before signing off with an F-bomb.
- 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 just 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 has been at pains to dampen anticipation surrounding his record chase this season, insisting that his priority remains helping the Lakers become a competitive outfit once more.
However, in recent days he has been more expansive when discussing the record, saying last week that 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 in the modern era.
"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."
Miami Heat coach Erik Spoelstra, who coached James to two of his four NBA championships in 2012 and 2013, said he had always assumed Abdul-Jabbar's record would never be beaten.
"I thought that would be untouchable," Spoelstra told NBA.com before James's record-breaking performance on Tuesday.
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.
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