The Gaza Strip has been under an air, land and sea blockade imposed by Israel and Egypt in 2007.
Visitors converged on the town's large Christmas tree in Manger Square, near the spot believed to mark Jesus' birthplace.
It had been unclear whether Israel would grant permits to members of Gaza's tiny Christian community to leave the Hamas-ruled coastal territory.
Archbishop Pierbattista Pizzaballa said he wanted to bring some holiday cheer to Gaza's Christians because it remains unclear whether they will be able to travel to Bethlehem in the West Bank for the holiday.
Unlike many other Christian families in the Bethlehem area, none of the Hosh siblings have moved abroad.
For decades, the people of Bethlehem have watched tour buses drive up to the Church of the Nativity, disgorge their passengers for a few hours at the traditional birthplace of Jesus, and then return to Israel.