Westwood made a name for herself as the queen of punk in the 1970s, with her androgynous designs and slogan t-shirts.
A representative said Dame Vivienne died on Thursday "peacefully, and surrounded by her family in Clapham, south London".
In a statement, her husband and creative partner Andreas Kronthaler said: "I will continue with Vivienne in my heart.
"We have been working until the end and she has given me plenty of things to get on with. Thank you darling."
Westwood was a sometimes-controversial punk and new wave designer in the 1970s and went on to dress some of the biggest names in the music and fashion industry.
Westwood is survived by her two children and second husband and creative partner, Andreas Kronthaler.
