Born in Zurich, raised in Switzerland and the United States (Lawrence, Kansas, and Grosse Pointe, Michigan) Rudolf came to Canada in 1967 to take degrees in English literature and journalism at Ottawa's Carleton University. A year of designing for the Tricycle theatre company in London, England, was followed by four years at the Ontario College of Art (two of which were spent with the off-campus program in Florence), graduating in 1978. He continued to study art in San Miguel de Allende, Mexico and at London's St.Martin's School of Art.

Exhibiting regularly in Canada and Europe, Stussi taught art in Toronto for various boards and groups and at OCAD.

From 1988 to 1991 he was president of the Canadian Society of Painters in Water Colour (CSPWC), founding the Diploma Collection, Canada's first national watercolour collection, and organizing International Waters, the first joint showing ever by the CSPWC, the English Royal Watercolour Society (RWS), and the American Watercolour Society (AWS), which toured all three countries.

In 1989 Stussi was artist-in-residence in Altos de Chavón in the Dominican Republic; in 1991 at Canada's renowned McMichael Collection.