The chat took place in the Santa Marta residence, the guest house in Vatican City where the pontiff lives.
Zuckerberg wore a dark suit and tie for the occasion while Ms Chan wore a black, knee-length dress.
The 32-year-old tech billionaire said on his Facebook page it was an honour to meet the pontiff.
“We told him how much we admire his message of mercy and tenderness, and how he’s found new ways to communicate with people of every faith around the world.”
He added: “It was a meeting we’ll never forget. You can feel his warmth and kindness, and how deeply he cares about helping people.”
Vatican spokesman Greg Burke said they discussed “how to use communication technologies to alleviate poverty, encourage a culture of encounter, and make a message of hope arrive, especially to those most in need”.
Also on Monday, Zuckerberg met Prime Minister Matteo Renzi and went for a jog around the Colosseum.
He discussed with the Italian premier last week’s earthquake, and how the Facebook community had helped.
Zuckerberg is in Italy for a conference at Rome’s Luiss university.
He and his wife spent their 2012 honeymoon in the Eternal City, flying there by private jet and staying in a luxury hotel near the Spanish Steps.
Article Appeared @http://news.sky.com/story/facebooks-mark-zuckerberg-and-wife-meet-pope-francis-at-vatican-10557509