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."
The Labour politician 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 went on to represent Glasgow Govan at Westminster until 1988.
He then took up the role of European Commissioner for Regional Policy and Cohesion in Brussels until 1995.
Mr Millan is survived by his wife Gwen, son Mark, daughter Liz and two granddaughters.