It is Jesus' 'Holy Towel' - once visited by pilgrims in the belief that it showed the face of Christ.
The religious relic was formed when Christ dried his wet head on a piece of cloth and left an indelible mark.
The 'Mandylion of Edessa' usually takes pride of place in the Pope's private Matilda chapel in the Vatican.
It is rarely seen in public and is one of the earliest images of Jesus - although there is scholarly disagreement about whether the facecloth is the original or a copy made 400 years after the life of Christ.
Now the British Museum has acquired permission to exhibit the Mandylion in Britain for the first time.
In June, the cloth will be the centrepiece of the museum's Treasures of Heaven exhibition, showcasing assorted Christian relics.
The museum is planning for vast crowds of Catholics, Russian Orthodox and Coptic Christians, in keeping with the levels of excitement that such relics can attract.
"This is one of the most extraordinary loans in recent memory," said the director of the British Museum, Neil MacGregor.
"The exhibition is all about trying to represent the universal human desire to reach out and touch the absolute."
The object was the subject of pilgrimages in the Middle Ages, say experts.
The cloth is among the most significant relics to be exhibited in Britain.
In 2009, the remains of Catholic nun St Therese of Lisieux arrived in Britain for a month-long tour.
The nun's remains had been preserved since her death in 1897 and attracted hundreds of thousands of pilgrims.
But such objects can have bizarre - and often unproven - links to Christ.
The Mandylion of Edessa is believed to have been created after King Agbar of Edessa (now the Turkish city Urfa) asked an unknown painter to go to the Holy Land to paint Jesus.
According to legend, the painter was unable to capture Christ's image because he was so dazzled by the light shining from his face.
Instead, Christ wiped his face on a towel after washing himself and left an image behind. When the cloth was returned to Agbar, it is believed to have cured him of leprosy.
Some believe the Vatican object is the original; others claim it is a copy created in the fifth century.
It is thought to have once been on display at Constantinople's Imperial Palace and transferred to the Vatican in the 14th century.