Several hundred people attended Regazzoni's funeral in Porza near Lugano, Switzerland.
Regazzoni, who drove for Ferrari from 1970-72 and 1974-76, was killed in a highway crash last Friday near Parma in northern Italy. He was 67.
After the church service, Regazzoni was to be buried in a family grave in Porza.
Gian Claudio "Clay" Regazzoni was born in Switzerland in 1939. He had been in a wheelchair since 1980, when he suffered spinal damage in a crash during the U.S. Grand Prix West in Long Beach, California.
During his career Regazzoni won the 1970 and 1975 Italian Grand Prix, the German GP in 1974, and the United States GP in 1976. He was second to Emerson Fittipaldi in the F1 championship in 1974.
Rescuers found the pilot of one of the two Su-34 fighters that had collided in midair in the Far East on January 18