The note was sent by the Pope's ambassador to the UK, Papal Nuncio Archbishop Antonio Mennini, to Archbishop of Glasgow Philip Tartaglia.
It states: "Having learned the sad news of the tragic accident which occurred in Glasgow when a police helicopter crashed into Clutha Vaults pub, close to the Cathedral, causing the death of several people and numerous injured, I would like hereby to convey to you, as Archbishop of Glasgow, the closeness of the Holy Father as well as my most sincere sympathy in these difficult moments.
"I assure you of my prayers for those who have tragically lost their lives or have been injured as well as their relatives. May the Lord grant eternal rest to those who have died and comfort their relatives and the entire community of Glasgow in these moments of distress and sadness."
Hundreds of people have signed a book of condolence laid out at Glasgow City Chambers. A silent queue formed yesterday as members of the public came forward to write their messages.
Among them was Kevin Lynch, 39, from Airdrie, a trainer with a charity which helps young people into training and employment.
"We have some of the young people with us, and they wanted to come down here and pay their respects. Everybody has been coming in feeling rather sombre, rather down and depressed.
"We talked amongst ourselves, my colleagues and I, and we felt it was it was fitting we pay our respects, both as an organisation and ourselves as well."
Another one who came to sign the book was 17-year-old Levi McDonald from Rutherglen. "I just wanted to pay my respects for the loved ones of the victims," he said.
Scottish Secretary Alistair Carmichael also signed the book.