His sons said: "Our dad was so much more than the name above the salon doors.
"He was a force of creativity, integrity, and love - for his work, for his team, and most of all his family.
"Whether you knew him as a hairdresser, a mentor, a colleague, or a friend, you'll know the warmth he brought to every conversation and the generosity with which he gave his time, his talent, and his heart."
They said they were heartbroken but promised to continue their father's legacy.
Miller was the first Scottish hairdresser to receive an OBE for services to hairdressing, presented by Her Majesty the Queen in 2012.
He was great friends with the late Sir Tom Farmer and famously cut his hair at the North Pole.
He was also three-time Scottish Hairdresser of the Year, Avant-Garde Hairdresser of the Year, and had two nominations for British Hairdresser of the Year.
Miller was also a judge for major competitions around the world, including the British Hairdressing Awards, L'Oréal Colour Trophy (UK and internationally), and Creative HEAD's Most Wanted Awards.
He also judged international titles such as Japanese, Dutch, and Norwegian Hairdresser of the Year.
In 2007, he began personally styling real-hair wigs for teenagers through the Teenage Cancer Trust and was instrumental in launching the 'Hair 4 U' initiative in Scotland, now operated by The Little Princess Trust.
He described himself as a "spiritual nomad", exploring paths through yoga, Buddhism, and Christian mysticism, and learned from the Dalai Lama - whom he gifted a tartan-pouched hair clipper in 1988.
A Charlie Miller spokeswoman said: "Charlie was not only a talented hairdresser but also a visionary leader whose passion, creativity, and commitment to excellence helped shape the careers of countless professionals across the industry. His work earned international recognition, and his salons became synonymous with quality, innovation, and style.
"Charlie's kindness, humility, and genuine love for people defined both his personal and professional life. He touched the lives of so many - from his loyal clients and trusted colleagues to the wider creative community."