Brick by Brick will support the Prince and Princess of Wales Hospice in its plan to move from its existing home in the city centre to a proposed new location at Bellahouston Park.
And it saw celebrities, businessmen and councillors come together to add their support.
Rhona Baillie, chief executive of the hospice, said: "We're asking the people of Glasgow to help us build their hospice.
"Not only will this enable us to further extend our existing services, it will allow us to provide much-needed provision of care to young people with life-limiting and life-threatening illnesses across the West of Scotland.
"We believe this development will be a major step forward in the provision of palliative care services to the people of Glasgow, and in particular will address a specific gap in the availability of care for young people who can be lost in the transition between children's and adult health services."
Rhona was joined at the launch by Carol, who hosts the hospice's annual fundraising event, (A Little Less) Strictly Come Dancing. She said she was thrilled to see the 3D plans and model for the first time, adding: "It's a stunning building and very sympathetic to the existing landscape.
"This is a fantastic opportunity for the people of Glasgow to throw their weight behind the Brick by Brick appeal and create a lasting legacy for the city."
An eight-acre site has been identified as the proposed new location for the hospice, which is being gifted to the people of Glasgow by Glasgow City Council.
Depute leader of the council, Archie Graham said he was "very impressed" by the hospice's ambitious vision. He said: "We've very excited about the proposal and recognise what a fantastic job the hospice does.
"Glasgow City Council donated the building at Carlton Place to the hospice 30 years ago and we're delighted to be able to support it again.
"The current facility is wonderful but the organisation has grown and needs something bigger and better for the modern age – what better space than here, adjacent to Bellahouston Park.
"Glasgow is rightly proud of this service and owes its staff and patients all the support, encouragement and friendship it can muster."
Over the years the existing hospice has been constantly adapted, but space is limited. The new building will allow it to expand and enhance services.
The new hospice designed by Glasgow architects NORD, will be a cluster of four "villas" which will include a 16-bed in-patient unit with direct access to a private garden space.
The in-patient unit and day services will promote greater patient choice with single rooms, allowing patients and families to have private space when they need it, and a social area which will ensure no-one feels isolated.
It will, for the first time, care for young people aged from 15.
Celebrity supporters and business leaders have also voiced their support for Brick by Brick.
Broadcaster Kaye Adams, who has been involved with the hospice for more than 10 years and is host of their annual ladies' lunch, said the hospice is a "tremendous asset" for Glasgow.
SHE said: "You build relationships with the people who work here and almost by osmosis you absorb the feeling and values of the place.
"The hospice is just an amazing place. I don't think the heart of this place will change in a new building, the passion and dedication will stay the same. It will just be allowed to work even more effectively."
Glasgow jeweller Stuart Laing, chairman of the Brick by Brick fundraising group, said he was honoured to have been asked to chair the appeal.
"The hospice needs to relocate so that the facilities and services it provides can be expanded to give Glasgow the hospice it deserves. I look forward to the challenge of the appeal and to witnessing the development of the new hospice."
Former chief executive of Scottish Enterprise Jack Perry is the chairman of the company set up to build the new hospice, Hospice Developments Limited.
He has been involved with the hospice for years after becoming an ambassador when he was a managing partner for accountancy firm Ernst and Young in Glasgow. He said: "The new site is terrific. I think it will be spectacular. It's not going to look like a hospital or a clinic."
Comedian Karen Dunbar, who has hosted a fundraising lunch and auction for the hospice, said it plays an "invaluable role" in Glasgow.
She said: "What they've got at the moment has been a wonderful facility but the new hospice is phenomenal.
"Patients and their families will have more space and access to the outdoors and I don't think we can underestimate how helpful that will be."
Presenter Heather Suttie said: "I am delighted to donate some of my free time to host events for people who'd like to help raise the £15million required to build this amazing new hospice."
River City star Libby McArthur said: "It's one of life's many paradoxes that the very joys of life are apparent in a hospice.
"Every time I visit I am struck by the power and the presence of it, the deep connections and love that pervades these places. Let's all help them expand."