Gilbert was born and raised in Montreal, Quebec, Canada; his last name is pronounced as in French (zheel-BAIR). He has always retained strong ties to that city, but his career has been international. After studies at the Quebec Conservatory in Montreal he went to Europe, where his teachers included Nadia Boulanger and Maurice Duruflé. Gilbert's harpsichord teacher in France was Italian-born Landowska protégé Ruggero Gerlin. In 1953 Gilbert won a major European organ prize, and for much of the first part of his career he was primarily occupied with that instrument. He served as organist and music director at the Queen Mary Road United Church (now Rosedale Queen Mary United Church) in Montreal for 15 years, designing and supervising the installation of a new organ there. From 1957 to 1974 he taught at the Quebec Conservatory.
In the early 1960s, Gilbert won financial support from the Quebec government and later from the Canada Council to return to Europe for research purposes, and he began to become familiar with the original engraved printings of some of the monuments of Baroque keyboard music. A four-volume Gilbert edition of François Couperin's keyboard works published between 1968 and 1972 was the first of a series of harpsichord publications, and from about 1965 onward, Gilbert's interests as a performer shifted to the harpsichord.
Although he lived mostly in France in the 1970s and 1980s, Gilbert was active all over Europe, in Canada (where he was richly garlanded with national honors), and in the U.S. He taught at several European conservatories and universities, and in 1988 he became the first Canadian, and one of few foreigners of any nationality, to hold the post of professor at the Paris Conservatoire. Gilbert's recordings have been released on the Harmonia Mundi and Archiv labels, as well as a host of more specialized lines. He has focused on French music, and his recordings of works such as the Premier livre de clavecin by Chambonnières are considered standards. But he has also made major Bach recordings, including, for example, a 1989 Archiv release on which he performed the Art of the Fugue.