The Journey, by renowned local sculptor Fenwick Lawson, was erected in 2008 to depict how monks brought the body of St Cuthbert to the city.
But the charity which paid for the artwork said its Millennium Place location had resulted in it becoming the target of late-night revellers.
It will now be moved to the grounds of nearby Durham Cathedral.
Trustees of The Journey charity, which will fund the move, called for the sculpture to be relocated after complaining it was being used as a "public urinal" by some who frequent nearby bars.
Canon Rosalind Brown, of Durham Cathedral, said: "It will have a new home in front of the cathedral on a widened path and our architects are working now on exactly how and when this will be done."
The sculpture pays tribute to the story of St Cuthbert's coffin.
The coffin was taken from Lindisfarne after monks fled from a Danish invasion. They transported it to different locations, ending at Durham Cathedral at the end of the 10th Century.
A £250,000 bronze sculpture is to be moved from its Durham city centre location to rescue it from vandals.