The triptych Mediterranean Sea View 2017 went under the hammer at Sotheby's on Tuesday after the artist donated them to help the children's hospital.
The triptych of paintings reference the European refugee crisis.
The works had been on display in the Walled Off Hotel that Banksy helped set up in 2017 in Bethlehem.
The trio of paintings were initially expected to fetch £1.2m when they appeared in Sotheby's Rembrandt to Richter evening sale.
The proceeds will go towards building a new acute stroke unit and buying children's rehabilitation equipment for the Bethlehem Arab Society for Rehabilitation.
The artist reworked three traditionally framed, romantic-era-style oil paintings depicting tumultuous seascapes, adding discarded life jackets and buoys, to produce the pieces.
They are seen as a reaction to Europe's migrant crisis of the past decade which has seen hundreds of thousands of people fleeing war and conflict and trying to reach the continent on dangerous journeys across the Mediterranean and Aegean seas.
Alex Branczik, Sotheby's head of contemporary art for Europe, said prior to the auction: "In Mediterranean Sea View 2017, Banksy corrupts three found oil paintings with his own witty reworkings to create something that, while posing as a 19th-Century seascape, spotlights one of the burning issues of the 21st Century.
"In Rembrandt to Richter, this triptych hangs in Sotheby's galleries alongside works by some of history's greatest landscape painters, including Bellotto, Van Goyen and Turner.
"Banksy's work, however, stands alone for its potent political message."
Banksy, whose Devolved Parliament painting depicting MPs as chimps was sold at auction in October for £9.9m, a record for the British artist, has addressed issues around refugees in previous works.
In 2015, he created a dystopian theme park, Dismaland, in the British seaside town of Margate featuring boats filled with migrants and an anarchist training camp.
In another work, The Son of a Migrant from Syria, the artist depicted Apple co-founder Steve Jobs, who was the son of a Syrian immigrant, carrying a knapsack and an Apple computer.
Banksy's latest stunt in the UK involved spraying a London Underground train carriage with messages about the spread of coronavirus.
Hours later, however, Transport for London announced that the artwork had been removed "some days ago due to our strict anti-graffiti policy". A spokesperson said Banksy was welcome to recreate his message "in a suitable location".
"We appreciate the sentiment of encouraging people to wear face coverings, which the vast majority of customers on our transport network are doing," the spokesperson said.
Asked what he thought of Western civilization, Mahatma Gandhi famously replied, “I think that would be a good idea.”