The exhibition, "Matisse Arabesque", runs until June 21st at the Scuderie del Quirinale, the former stables of Italy's presidential palace which have been transformed into a museum that boasts spectacular views over the Eternal City.
Curator Ester Coen has set out to demonstrate how Matisse's enduring fascination with what he would have referred to as the Orient influenced the work of an artist considered one of the fathers of modern art.
In particular, a love of arabesque - designs based on the intertwined, flowing lines of early Islamic art - had a huge influence on how Matisse (1869-1954) came to think about perspective and space in his painting.
Late in his life, the Frenchman reflected that his education had involved a gradual realisation that he had to "forgot the technique of the Masters or rather to understand it in a completely personal way.
"Next came the knowledge and influence of the arts of the Orient," he said.
Matisse also once said that modern art, "in its very essence is closer to archaic and primitive arts than to the arts of the Renaissance."
Those ideas form the basis for the exhibition and Coen illustrates the point by accompanying Matisse's paintings with examples of the kind of decorative arts from which the artist took inspiration, among them Moorish tiles, African masks, shields and wood carvings, and textiles from places as far afield as Uzbekistan and Japan.
The exhibition also underlines the huge impact that the time Matisse spent in Morocco in 1911-12 had on his subsequent career.
Works such as "Zorah on the terrace", one of a number on loan from Moscow's Pushkin museum, and "Moroccan Garden" (from New York's MoMA) illustrate some of the motifs and techniques which were to recur in his work for decades.
The Pushkin has also provided "Goldfish", arguably the best known of the paintings on display in Rome.
Art historians believe that masterpiece was less obviously inspired by the time Matisse spent in Tangiers, where he registered his admiration for the locals' capacity to spent hours gazing into goldfish bowls in quiet contemplation.
The "Moorish Screen", from the Philadelphia Museum of Art, provides the most obvious demonstration of Matisse's admiration for the decorative traditions of North Africa and the Middle East and his willingness to incorporate them into contemporary scenes, enhancing a magical quality to his work at the expense of realism.
The collection of more than 100 works had been put together in collaboration with some of the world's leading museums: The Tate in London, New York's Met and the Pompidou Centre in Paris, as well as the Pushkin, the Hermitage in St Petersburg and MoMA.
"There are some exceptional paintings here and it was very difficult to get them released," said Coen. "That makes it all the more important to have this opportunity to breath the air of the Orient and to appreciate the Islamic art that Matisse brought to Paris."