Her death was made public by Stella Schnabel, daughter of painter and film director Julian, who said she had "never met a woman quite like" her.
"Go in peace my Roman mother," she wrote on Instagram.
Pallenberg was the girlfriend of Brian Jones but left him for fellow Rolling Stone Keith Richards.
She was also alleged to have had an affair with Sir Mick Jagger while they were making 1970 film Performance, though she always denied it.
Born in Rome in 1944 to German and Italian parents, Pallenberg began her career as a model and spent time in the 1960s at Andy Warhol's famous Factory.
She met Jones in 1965 but left him two years later for Richards. Jones went on to leave the band and died shortly afterwards.
In his autobiography, Life, Richards described Pallenberg as a "very strong" woman who was "extremely bright" and "a great beauty".
The couple had three children together, one of whom died as an infant, before they finally separated in 1980.
Pallenberg sang backing vocals on classic Stones track Sympathy for the Devil and was said to have had a "profound" influence on the band by their one-time PA Jo Bergman.
She had roles in films including 1969's Barbarella and 2007's Mister Lonely, and made a cameo appearance in BBC sitcom Absolutely Fabulous in 2001.
Pallenberg was accused of manslaughter in 1979 after a man named Scott Cantrell killed himself with her gun in the New York home she shared with Richards.
"I didn't feel anything," she said of the death, for which she was subsequently cleared. "That's one of the wonders of drugs and drink."
Known for her colourful lifestyle and fascination with black magic, Pallenberg sought help for her addictions in 1987 and went on to study fashion at Central St Martins in London.
She is survived by her two children and five grandchildren.
Follow us on Facebook, on Twitter @BBCNewsEnts, or on Instagram at bbcnewsents. If you have a story suggestion email entertainment.news@bbc.co.uk.
Anita Pallenberg, the model and actress best known for her relationships with members of the Rolling Stones, has died at the age of 73.