Twombly, who had cancer, died in Rome, said Eric Mezil, director of the Lambert Collection in Avignon, France, where the artist opened a show in June. Twombly had mostly lived in Italy since 1959.
"A great American painter who deeply loved old Europe has just left us," French Culture Minister Frederic Mitterrand said in a statement. "His work was deeply marked by his passion for Greek and Roman antiquity, and its mythology, which for him was a source of bottomless inspiration."
Twombly was known for his abstract works combining painting and drawing techniques, repetitive lines and the use of words and graffiti. He is often linked to the legendary American artists Jasper Johns and Robert Rauschenberg.
In 2010, he painted a ceiling of the Louvre museum in Paris, the first artist given the honor since Georges Braque in the 1950s.
For that work he chose something simple: a deep blue background punctuated with floating disks and emblazoned with the names of sculptors from ancient Greece, apt for a gallery of bronzes.
"I got into something new in old age," he said of his choice of color, which was unusual.
The Lexington, Virginia-born artist said he was inspired by the colors he found in a Chinese print as well the blue of early Italian Renaissance artist Giotto, who used paint made from lapis lazuli.
"I was just thinking of the blue with the disks on it, it's totally abstract. ... I put all the great Greek sculptors' names on the top. It's that simple," Twombly told The Associated Press at the time.
Simple or not, his work fetched millions at auction: In 2002, an untitled Twombly painting set an auction record for the artist at Sotheby's, fetching euro5.6 million. Before that, a 1990 Christie's auction set a record for Twombly, with his 1971 untitled blackboard painting fetching $5.5 million.
"In painting, drawings and sculpture, Cy Twombly constantly held himself apart from the great conflicts that would upset the artistic scene of the 20th century," Mitterrand said.
His work ignited the passions of his followers. In 2007, a woman was arrested in France for kissing an all-white canvas he painted, worth about $2 million. Restorers had trouble getting the lipstick off and she was ordered to pay hundreds of dollars to the owner and the gallery - and $1.50 to the artist himself.
Mezil, the Avignon gallery director, said his show there was "the most beautiful exhibit before his death."
Twombly, who had a gallery in his name at the Menil Collection museum in Houston, Texas, won a series of awards, including a knight in France's Legion of Honor bestowed at the inauguration of the Louvre ceiling.
He won Japan's highest and most prestigious art award in 1998, the Praemium Imperiale prize, which honors fields not covered by the Nobels.
In 2001 he snapped up the prestigious Golden Lion award at the Venice Biennale.
Born in 1928, Twombly studied in Boston, New York and North Carolina at the height of Abstract Expressionism, according to the Tate Modern where he had a show in 2008.
Associated Press writer Cecile Brisson in Paris and Dolores Barclay in New York contributed.