Archbishop Chrysostomos II said the Menil Collection plans to return the Byzantine frescoes early next year after the church insisted that they not "allow them to remain there even for one second longer."
"I salute this decision by the Menil Collection because embarking on a court battle would honor neither us nor the Collection," the Archbishop said.
Antiquities smugglers looted the frescoes from the Ayios Themomianos church in northern Cyprus following a 1974 Turkish invasion that split the island into a Turkish-speaking north and a Greek-speaking south.
Menil Collection founder Dominique de Menil obtained the frescoes in 1983, and struck an agreement with the Cyprus church to keep and exhibit them at a purpose-built chapel in Houston.A decade later, the Cyprus church granted the museum a loan extension until February 2012 in recognition of its efforts to reassemble and restore the fragmented frescoes.
Another section depicts the Virgin flanked by Archangels Michael and Gabriel.
The Cyprus Antiquities Department will oversee the transportation of the frescoes back to Europe, department Director Maria Hadjicosti said.
The church says scores of religious artifacts, including icons and mosaics, were looted from Greek Cypriot churches in the island's north.
Many have since appeared on the international art market. Chrysostomos said "millions" have been spent purchasing them with the purpose of repatriating them. The church's biggest success was the recovery of several priceless 6th century mosaics.
"We'll rest only when all our antiquities, all our ecclesiastical objects return to where they belong," he said.
Christianity in Cyprus stretches to the faith's earliest years. The Apostle Paul is said to have preached the gospel in Cyprus in A.D. 45 and converted the island's Roman governor Sergius Paulus — the first Roman official to undergo conversion.