Several media reports stated that Paula Podest Ruiz, 39, and Carlos Ciuffardi Elorriga, 41, who had a civil union eight years ago, told the pope a religious ceremony that was to follow was cancelled after their parish church in Santiago was heavily damaged in an earthquake in 2010.
The magnitude 8.8 quake caused widespread damage and triggered a tsunami, resulting in the loss of more than 500 lives.
"We told him that we are husband and wife, that we have two daughters and that we would have loved to receive his blessing. All of a sudden, he asked us if we were married for the Church too," said Ciuffardi.
"He liked us and he asked: 'Do you want me to marry you?'"
"Yes of course,' we said."
The pope performed the brief ceremony in the front of the plane.
An improvised marriage certificate was signed by the pope, the couple, and a bishop who was on the plane Cueto.