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The 20-foot sculpture was unveiled during mass on the 105th World Day of Migrants and Refugees on Sunday.
Depictions of Christ's parents Mary and Joseph have been included in the piece.
Pope Francis once famously likened the journey of Joseph and Mary to Bethlehem to the migrations of millions of refugees fleeing wars.
Mr Schmalz, whose past creations include 'Homeless Jesus Christ' - depictions of Jesus sleeping rough on benches outside cathedrals - said his latest piece took a year of working "obsessively, from 4 in the morning".
"Angels Unaware" is facing in a direction intended to portray the boat sailing towards St. Peter's Basilica, he said.
"It's one thing to say you're being welcoming but to show it with a piece of bronze artwork in St. Peters Square is really powerful," he said.
"This is not a museum here."
The sculptor said Pope Francis made his appreciation clear.
"He put his two hands on his heart, looked at me for a moment," he said.
"That gesture, he really showed to me how much he thinks this is a suitable sculpture to promote his ideas."
Vatican sculpture dedicated to migrants unveiled, BBC News, 30 September 2019