Corbelli was born in Turin, Italy in 1952 and studied with Giuseppe Valdengo and Claude Thiolas. He made his debut in 1973 (at the age of twenty-one) in Aosta, Italy as Monterone in Verdi's Rigoletto. Subsequently he appeared at La Scala in Milan (singing in all three of the Mozart/Da Ponte operas under conductor Riccardo Muti), and also in such cities as Turin, Verona, Bologna, Florence, and Naples, as well as major opera houses in Switzerland, France, Austria, Germany, England, Spain, Israel, and North and South America. At the beginning of his career Corbelli sang lyric baritone roles, but his natural talent for comedy caused him eventually to be typecast in comic parts. Among the buffo roles he has performed and/or recorded are Dr. Bartolo in Rossini’s Il barbiere di Siviglia, Taddeo in Rossini’s L'italiana in Algeri, Don Geronio in Rossini’s Il turco in Italia, Dr Dulcamara in Donizetti’s L'elisir d'amore, and the title role of Donizetti’s Don Pasquale. He has frequently showed his versatility by singing two roles from the same opera: Figaro and the Count in Mozart’s Le nozze di Figaro, Leporello and the title role in Mozart’s Don Giovanni, Guglielmo and Don Alfonso in Mozart’s Così fan tutte, and Dandini and Don Magnifico in Rossini’s La Cenerentola, among others.
At the Royal Opera House, as of March 2012, Corbelli had taken part in 87 performances since his debut in 1988 (as Taddeo in L'Italiana in Algeri). Corbelli's roles at the Royal Opera House have included Don Alfonso in Così fan tutte (8 perf., 1997), Doctor Malatesta in Don Pasquale (8 perf., 2004; 5 perf. 2006), Don Magnifico in La Cenerentola (10 perf. 2007-2008), Doctor Bartolo in Il barbiere di Siviglia (6 perf., 2009), and Michonnet in Adriana Lecouvreur (8 perf., 2010).
At the Metropolitan Opera House in New York, Corbelli performed 64 times, as of March 2012, since his debut in 1997, appearing 26 times as Dandini, 7 times as Dulcamara in L'elisir d'amore, 15 times in the title role of Gianni Schicchi, 8 times as Sergeant Sulpice in La Fille du Regiment, and 8 times as Taddeo in L'Italiana in Algeri.
Although primarily associated with Italian-language comic roles, Corbelli’s résumé shows his wide-ranging interests and versatility, including French and German roles (Sulpice in Donizetti's La fille du regiment, Papageno in Mozart’s Die Zauberflöte), Baroque opera (Seneca in Monteverdi’s L'incoronazione di Poppea) and a twentieth-century English-language opera (Nick Shadow in Stravinsky’s The Rake's Progress). He has also sung roles in later Italian comic operas, for instance the title roles in Verdi’s Falstaff and Puccini’s Gianni Schicchi. He is active in the concert hall as well, performing as a soloist in oratorios and vocal symphonies.
On 26 November 2007, while in London rehearsing for La Cenerentola, Corbelli stepped in at the last minute for a production of L'elisir d'amore at the Royal Opera House, singing the role of Belcore for the second half of the opera from the side of the stage while Ludovic Tézier, who had sung the first half with a throat infection, acted the role.
Although in recent years Corbelli has sometimes been billed as a bass-baritone, he has insisted that he is a baritone. Corbelli's voice is not large, but its dark coloring gives it power and heft. He possesses a tight vibrato and great flexibility in coloratura and patter. His diction is always razor-sharp and he points up the text brilliantly, particularly in recitatives. His stage presence is commanding and he excels in comic timing and subtle characterization.