MacMillan, who was born in 1928, died suddenly on Saturday, August 16 in Inverness during the Royal Incorporation of Architects in Scotland's (RIAS) Andrew Doolan Awards, which he was chairing.
His family are planning to hold his funeral in private. Details of an event to celebrate his life will be announced shortly.
RIAS President, Iain Connelly, one of the Awards judges, said: "Andy was a great architect, an educator of international renown and one of the finest human beings it has been my privilege to know.
"His influence on generations of students at the Mackintosh School of Architecture and in the many other institutions where he taught, was immense.
"Andy's contribution to Scotland was among the most significant of any architect in the post World War II era. He will be remembered as someone who lived life to the full, who inspired all those he taught and all those who encountered him, as an individual of enormous talent, tremendous enthusiasm and irrepressible fun. Andy's legacy is the hugely improved built environment of Scotland wrought by his own hand and those of successive generations of his students. He will forever be missed."
Professor Tom Inns, director of the Glasgow School of Art, expressed the feelings of the whole GSA community on hearing the sad news that Andy MacMillan had passed away: "We were saddened to hear the news that Andy MacMillan had passed away.
"Andy's association with the GSA spanned more than seven decades from student to Head of the Mackintosh School of Architecture and latterly as Emeritus Professor. He was one of the greats of post-war British architecture and his legacy is visible not only in his buildings but in the lives and work of generations of architects whom he taught, challenged and enthused.
"He was a generous, inspirational man and everyone who met him came away better for having done so. We will miss him greatly and our thoughts are with Angela and the family at this very sad time."
MacMillan is survived by his wife Angela, their three daughters, their son and three grandchildren.
His family have asked those who wish to mark his memory to donate to the restoration fund for St Bride's Church, East Kilbride.