The piece — “Mobile Lovers” — which shows a couple embracing while gazing at their phones, appeared on the wall of the Broad Plain Boy’s Club in April.
It was attached to a piece of wood and screwed onto the wall, so youth club members were able to remove it with a crowbar and sell it.
Banksy confirmed that the club, which is based in the southwestern city of Bristol, owned the artwork in a rare letter to owner Dennis Stinchcombe.
The 120-year-old club sold it to a private collector for £403,000, more than three times what the centre needed to save it from closure.
Stinchcombe told a news conference on Wednesday that the club was “incredibly lucky” to have had the piece donated by the artist.
“Within 12 months we could have well been closed, which means 120 years of exceptional youth work in Bristol would have been lost.
“That would have been a tragedy for Bristol… Banksy came along at the right time.”
Members of the youth club decorated the wall where the painting had been with a mural reading: “Thanks Banksy”.
Banksy is believed to have started out as a graffiti artist in the city, although the artist’s identity remains shrouded in secrecy.
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