Born in Milan in 1931, Vignelli trained as an architect in Milan and Venice. He met his wife, Lella, at an architects' convention and the pair married in 1957 – they would go on to become design and business partners.
Vignelli visited America in the 1950s first on a fellowship and then to teach, before returning to Milan to start his first design and architecture business with his wife.
In the mid-1960s the couple moved to New York and Massimo Vignelli became a founding member of Unimark International in 1966, which quickly became one of the world's biggest design companies.
He was responsible for some of the company's most recognisable and significant work including the corporate identity for American Airlines. Together with Unimark partner Bob Noorda, Vignelli designed the distinctive signage for the New York subway – still in use today – followed by Vignelli's subway map, which was loosely based on the principals of Harry Beck's London Underground map. He also designed the signage and way finding for the Washington DC Metro.
Writing about Vignelli's New York subway map on the occasion of its digital relaunch in 2011, New Yorker critic Paul Goldberger described it as "a nearly canonical piece of abstract graphic design".
Vignelli became frustrated with the company and left to set up Vignelli Associates in 1971 with Lella, followed by Vignelli Designs in 1978.
In 1982 they were awarded the American Institute of Graphic Arts (AIGA) gold medal.
"Not only do the Vignellis design exceedingly well, they also think about design," said the AIGA citation. "It is not enough that something — a chair, an exhibition, a book, a magazine — looks good and is well designed. The 'why' and the 'how', the very process of design itself, must be equally evident and quite beyond the tyranny of individual taste."
Other awards have included the American Institute of Architects' industrial design medal (1973), and the first US Presidential Design Award, presented by Ronald Reagan in 1985 for Vignelli's work on the American National Park Service Publications Program.
In 2003, he was given the National Lifetime Achievement Award from the National Museum of Design at Cooper-Hewitt, New York.
Vignelli's work has been exhibited and added to the collections of major art institutions including New York's Museum of Modern Art, the Metropolitan Museum of Art and the Cooper-Hewitt design museum.
Pentagram partner and former Vignelli employee Michael Beirut paid tribute to the designer.
"He was able to bring enthusiasm, joy and intensity to the smallest design challenge," wrote Beirut in Design Observer. "Even after fifty years, he could delight in designing something like a business card as if he had never done one before.
"It was Massimo who taught me one of the simplest things in the world: that if you do good work, you get more good work to do, and conversely bad work brings more bad work. It sounds simple, but it's remarkable, in a lifetime of pragmatics and compromises, how easy it is to forget: the only way to do good work is simply to do good work. Massimo did good work."
Vignelli's family announced he was gravely ill earlier this month, when his son Luca issued a public invitation to anyone who had been inspired by Vignelli and his work to write him a letter.
Vignelli died at his home in Manhattan on Tuesday morning and is survived by his wife, his son and daughter, and three grandchildren.
Portrait of Massimo Vignelli is by John Madere.