The statue, by Canadian sculptor Timothy Schmalz, is a life-size bronze of a shrouded person sleeping on a bench, with only the crucifixion wounds on his feet indicating he represents Jesus.
Glasgow will be the first location in Scotland to house the statue, which is found in around 50 locations across the globe including the Vatican, Madrid in Spain, Chennai in India and several cities in the US.
Mr Schmalz approached Father Willy Slavin, former parish priest in St Simon's Church in Partick and former chair of Glasgow Emmaus, to bring the message to Glasgow.
The sculpture will be installed in November on the pavement in Nelson Mandela Square, beside St George's Tron church.
Father Slavin worked on the project with the inter-faith group Glasgow Churches Together.
He said: "The sculpture has a strong message and it is right that more attention is brought to homelessness. With as many groups as possible getting involved, the sculpture will arrive in November."
The £25,000 cost of the Glasgow Homeless Jesus initiative will be met by donations from individuals and pro bono work from architects and other contractors, organisers said.
So far £10,000 has already been raised and organisers stress no funds will be diverted from front-line charitable work to help the homeless.
The sculpture has met with controversy elsewhere, with some people in the US protesting against it as they felt it might encourage the homeless to gather nearby.
Elspeth Glasgow, of Churches Together Glasgow, said: "It was brilliant when we were given approval for this plan.
"We had to take great care in our proposal, given some of the stories of other cities not giving it permission."
The sculptor's inspiration for the statue comes from the gospel of Matthew 25: 31-46 - "Truly I tell you, whatever you did for one of the least of these brothers and sisters of mine, you did for me."
