His family said he died at Glasgow’s Southern General Hospital on Thursday died on Thursday night from bronchial pneumonia. He had recently been diagnosed with cancer.
Born in Dundee, Mr Millan was elected MP for Glasgow Craigton at the 1959 General Election and held that seat and, after its abolition Glasgow Govan, until 1988.
He served in the Wilson Government of 1964–70 as Under-Secretary of State for the Air Force from 1964 to 1966, and as Under-Secretary of State for Scotland from 1966 to 1970, and in the Callaghan government of 1976–1979 as Secretary of State for Scotland.
When he stood down from Westminster in 1988, he took up the post of European Commissioner for Regional Policy and Cohesion.
The SNP's Jim Sillars took his seat in the memorable Glasgow Govan by-election of 1988.
In 1999–2001, Mr Millan chaired the Millan Committee which proposed reforms to the provision of mental healthcare in Scotland.
Mark Millan, 56, described his dad as someone who "very much loved and looked after his children and grandchildren.
"He always found the right balance for political commitments and his love and care for his family. He was very much involved and generous with his family and his time. He was a great dad."
Tribute was also paid by Scottish Labour's Lord Foulkes of Cumnock who said: "Bruce was someone of whom the Labour Party should be very proud. He was a great public servant and a very modest man.
"He served with great distinction as Secretary of State and as a European Commissioner and he will be very sadly missed by all of us within the Labour family."
Ed Miliband MP, leader of the Labour Party, said: "Bruce Millan dedicated his life to service of our country and the Labour Party. I am very sad to hear news of his passing.
"As a minister he served in two Labour governments, including as Secretary of State for Scotland and also served as a European Union Commissioner.
"Even in retirement, he still showed his determination to make a difference when he chaired an inquiry into mental health on behalf of the Scottish Government.
"Our thoughts are with his family, he will be missed by many friends in the Labour Party."
First Minister Alex Salmond said: "My thoughts and condolences are with Bruce Millan's wife, family and friends at this sad time.
"Bruce was dedicated to public life, serving Scotland as a respected parliamentarian and as Commissioner in Europe.
"As Scottish Secretary in the Callaghan government, his distinguished career spanned major political events in modern Scottish history.
"He was held in high regard across the political spectrum, and will be missed by his many friends and colleagues."
Mr Millan is survived by his wife Gwen, son Mark, daughter Liz and two grand-daughters.