She died at home on Thursday after a short illness.
The duchess is survived by her husband of three years, Alfonso Diez, who is 25 years her junior.
The Duchess of Alba was the head of one of Spain's oldest noble families.
The frizzy-haired eccentric aristocrat was one of Spain's most-loved figures whose antics filled the nation's gossip magazines and gripped the audiences of TV chat shows even during the final months of her long life.
Described as the "rebel noble", she spurned convention to forge her own path in life, following her passion for flamenco and, as a patron of the arts, amassing a private collection of masterpieces said to rival any in Europe.
Her exuberant character, complete with squeaky voice and flamboyant dress-sense, enraptured Spaniards who followed the vicissitudes of her 88 years.
The Duchess of Alba, seen here in 1947, had bequeathed her inheritance to her six children
Once a famed beauty who turned down a request to be Picasso's
muse, she shocked the establishment when she married her confessor, a
defrocked Jesuit priest, in 1978, six years after the death of her first
husband with whom she had six children. But it was her third marriage to a civil servant 25 years her junior in 2011 that provoked an even bigger scandal, a union that was opposed by her children as well as King Juan Carlos of Spain, but that was welcomed by Spaniards as a colourful drama.