Mobile Lovers, showing two lovers embracing while checking their phones, was attached to a plank of wood screwed on to a wall in Clement Street, Bristol.
It was removed from the wall, believed to be owned by Bristol City Council, hours after its location was discovered by workers at the nearby Broad Plain & Riverside Youth Project.
The youth club, run by Dennis Stinchcombe MBE, 58, installed the piece in a corridor .
Mr Stinchcombe had planned to sell Mobile Lovers to raise funds for the youth club, which is attended by 1,000 youngsters and requires £120,000 to survive.
But after speaking to officers from Avon and Somerset Police, the youth club decided to hand the piece to Bristol City Council.
George Ferguson, the mayor of Bristol, said the piece would go on display at the City Museum and Art Gallery.
A screen print of Mobile Lovers has been installed in the artwork's original home, a boarded-up doorway overlooking the busy A4032 road into Bristol's centre.
The discovery of Mobile Lovers comes days after a piece depicting three 1950s-style agents listening in on conversations in a telephone box appeared on a house in Cheltenham.