That is nearly double the price of his previous most expensive work, bought by the same person a year ago.
It has broken several other records including becoming the most expensive work by any US artist.
It is also the highest price fetched for any art by a black artist and the first piece created since 1980 to break the $100m mark.
The untitled work was done in oil stick, acrylic and spray paint, and depicts a face in the shape of a skull.
It was sold to Yusaku Maezawa, a 41-year-old Japanese fashion entrepreneur who plans to set up a museum in his home town of Chiba.
Bidding for the piece during the auction at Sotheby's lasted 10 tense minutes. Cheers and applause erupted in the room when the work was sold to Mr Maezawa by telephone.
He later posted on Instagram that the painting made him feel "so much excitement and gratitude for my love of art", a feeling he wished to share with "as many people as possible".
Mr Maezawa last year set the previous record for a Basquiat piece, when he paid $57.3m for a painting of a horned devil.
Basquiat, a native New Yorker, died in 1988 of a heroin overdose aged 27. He had been an artist for just seven years.
Most of his works depict the problems faced by African Americans in the US, reports the BBC's Laura Bicker in Washington.
Once a graffiti rebel from Brooklyn who sold drawings for $50, he is now in the same league as Pablo Picasso and Francis Bacon, she says - part of a rare group of artists whose work has sold for more than $100m at auction.
"Breaking $100m for a work which is that recent is definitely extraordinary," said Gregoire Billault, head of contemporary art at Sotheby's.
"I think it just speaks about the talent of this guy. It's just pure emotion. He's bringing something never seen before."

Police were first called to St James Boulevard in Newcastle just after midnight due to concerns for a man, 21, and an 18-year-old woman.
Her condition is described as potentially life-threatening.
An hour later, another couple, both 18, also had to be taken to hospital after becoming ill in the city centre.
Northumbria Police said a quantity of drugs, believed to be ecstasy, had been seized and inquiries were ongoing.
Det Inst Sally MacDonald said: "Taking illegal drugs is incredibly dangerous and the fact four people have been taken ill in just one evening is particularly worrying."

Secret service and regular police have been searching for Ivan Kaspersky, 20, for at least two days, a police source told Interfax news agency.
His father's firm, Kaspersky Lab, told a newspaper it could not confirm news he had been abducted.
Yevgeny Kaspersky made his fortune developing anti-virus software.
News of his son's abduction was reported by Russian news website Life News, quoting its own sources.
The kidnappers are demanding 3m euros (Â£2.6m; $4.3m) for Ivan's safe return, the website says.
According to the unconfirmed report, he was snatched while on his way to work in Moscow on Tuesday.
When contacted by Russian newspaper Gazeta, Kaspersky Lab said it could neither confirm nor deny the report.
There has been no official comment on the story.
Kaspersky Lab is regarded outside Russia as one of the country's few business success stories not related to the energy sector.
The US business magazine Fast Company recently ranked Kaspersky Lab among the Top 50 Most Innovative Companies worldwide.
A painting by the late artist Jean-Michel Basquiat has sold at auction in New York for $110.5m (Â£85.4m).
[NEXT_CONCEPT]
Four people had to be treated in hospital after taking what is thought to be ecstasy.
[NEXT_CONCEPT]
The son of Russian software entrepreneur Yevgeny Kaspersky has gone missing in Moscow and may have been kidnapped, Russian media report.