Mr MacMillan, 85, died 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.
Mr MacMillan was best known for his collaborative work with Isi Metzstein and together they were responsible for the A-listed St Peter's Seminary in Cardross. An ex-student of the Glasgow School of Art, went on to head up the Mackintosh School of Architecture and latterly was emeritus professor at the institution.
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. 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, said: "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."
Mr MacMillan is survived by his wife Angela, their three daughters, their son and three grandchildren.
His family ask those who wish to mark his memory to donate to the restoration fund for St Bride's Church, East Kilbride, a building which he and Metzstein designed.