The father of three served as Education Minister and Environment Minister in Scotland before standing down from politics in 2001 for health reasons
Mr Galbraith, who is believed to have been the world's longest-surviving lung transplant recipient, died in hospital in Glasgow yesterday from an infection.
The former neurosurgeon received the transplant in 1990 at the Freeman Hospital in Newcastle.
Former Labour chancellor Alistair Darling issued a statement on behalf of Mr Galbraith's family.
He said: "Sam was a brilliant neurosurgeon, a dedicated politician and a very dear friend. But above all, he was devoted to his family, to Nicola and their three daughters - Mhairi, Heather and Fiona - who are foremost in our thoughts.
First Minister Alex Salmond described Mr Galbraith as "a devoted and gifted politician whose commitment to improving the lives of others never wavered, even though he faced living with his own serious health condition for the best part of 25 years."
Scottish Labour leader Johann Lamont also paid tribute to him and said: "Sam was a wonderful man. A great doctor, an inspiring colleague and dedicated family man.
"Sam was a great champion of the NHS, and he himself was a great example of how it can transform lives. We will all miss his vigour, his support and his candour."
Former Prime Minister Gordon Brown said: "Sam Galbraith was great in every respect - a great surgeon, a great statesman and a great family man who will be sorely missed."
Liberal Democrat Lord Jim Wallace, who was deputy first minister in the coalition Scottish Executive that included Mr Galbraith, said he was "very saddened" by his death.
He added: "It was a privilege to work alongside him in coalition and I very much wish to recognise the significant contribution he made in helping our fledgling Parliament to mature and work well for Scotland."