Mr Millan, 85, served as Labour MP for Glasgow Craigton and Glasgow Govan and was a European Commissioner in Brussels.
He was diagnosed with cancer and died from bronchial pneunomia at Glasgow's Southern General Hospital.
His son, Mark, 56, described him as a "wonderful caring father".
He added: "He always found the right balance for political commitments and his love and care for his family."
Bruce Millan was born in Dundee and served as an MP in Glasgow for 29 years. He was first elected to represent Glasgow Craigton in 1959 and after that seat was abolished he represented Glasgow Govan at Westminster until 1988.
He then became European Commissioner for Regional Policy and Cohesion until 1995.
First Minister Alex Salmond said: "As Scottish Secretary in the Callaghan government, his distinguished career spanned major political events in modern Scottish history."
Mr Millan is survived by his wife Gwen, son Mark, daughter Liz and two granddaughters.