Ms Wilson, who was born in Cambridge but grew up in the Borders and was educated in Jedburgh made her international reputation at Central Saint Martins, at the University of the Arts London.
Among the countless students whose careers she helped shape were Christopher Kane, Stella McCartney and Alexander McQueen.
She was reported to have died in her sleep during a visit to her sister in Scotland.
A profile of Ms Wilson three years ago observed that she was "the single most well-known fashion educator, certainly in this country, if not the world."
Central Saint Martins said in a statement that it was "devastated" by news of her death.
It added: "Louise has been an inspirational person both within the college and the wider world of fashion.
"Since becoming Course Director for MA Fashion in 1992 she has taught a huge proportion of the world's leading fashion designers and her course continues to produce talented ground-breaking graduates.
"Her commitment to her students and passion for creative excellence are legendary. Her deep understanding of fashion and her drive for funding for bursaries, facilities and opportunities are part of what made her such an extraordinary educator."
Stella McCartney was one of many figures in fashion who tweeted their condolences.
She wrote: "What an inspiration. I send my deep sympathy to your family. No one will ever replace you because you were a true one off. Louise we will all miss you r.i.p xx stella"
She received an OBE in 2008 for her services to fashion and to education and is survived by her partner Timmi and their son, TJ.