Westwood's official Twitter account broke the news on Thursday, saying the fashionista had "died today, peacefully and surrounded by her family, in Clapham, South London."
"The world needs people like Vivienne to make a change for the better," the statement added.
Her husband and creative partner Andreas Kronthaler also said: "I will continue with Vivienne in my heart."
Westwood was known for helping to bring punk and New Wave fashion to the British mainstream, through her business partnership with Sex Pistols manager Malcolm McLaren.
Like the nihilistic punk band, Westwood's clothes were often intended to shock as well as convey a political message. However, she also designed timeless pieces of high fashion worn by celebrities and even royalty.
Westwood was also extremely politically active, fighting for causes including nuclear disarmament, vegetarianism, and the release of persecuted whistleblowers and journalists such as Chelsea Manning and Julian Assange.
"Our sympathies go out to the family and friends of Vivienne," WikiLeaks tweeted in response to news of her death. "She was a great friend and a hero who was always true to her heart and beliefs. To the end. You will be forever missed."
Westwood (was born into a working-class family in Cheshire, UK, in April 1941. Although she briefly studied jewelry making and silversmithing at the University of Westminster in 1958, she gave up on the art world and studied to become a schoolteacher, although she still sold homemade jewelry on the side.
Творения учеников Вивьен Вествуд на модном показе в аэропорту Темпельхоф в Берлине
© AP Photo / Fritz Reiss
She married Derek Westwood, a factory apprentice, in 1962, and gave birth to a son, Benjamin, the following year. However, that ended when she met McLaren a few years later. They also had another son, Joseph, in 1967.
The duo proved key to Westwood's success, with her making clothes he designed, which the Sex Pistols band members then wore. Their punk rock boutique shop, SEX, became a punk mecca from 1974 until 1976. The acclaim brought her an international audience, and her designs won spots in art galleries, fashion shows, and custom commissions for everyone from Virgin Galactic to King's College London.
She married Andreas Kronthaler, a former student of hers, in 1992.