He passed away on Friday (11Sep09) from heart failure at the Barrie Memorial hospital in Montreal, Canada.
Cossette served in the army during World War II before moving into showbiz. He produced a number of shows for the New York stage including the six-time Tony Award-winning The Will Rogers Follies.
The star was instrumental in bringing the annual Grammy Awards to television and paid $150,000 (£100,000) in the 1970s for the right to broadcast the ceremony.
Cossette has a star on the Hollywood Walk of Fame and was inducted into Canada's Walk of Fame in 2005, the year he retired.
Neil Portnow, president of the Recording Academy, says in a statement, "It is with a heavy heart that we say goodbye to our dear friend and the father of the Grammy awards. Pierre was a creative visionary and one of the most accomplished, versatile and respected producers. It was because of his passion and dedication that the Grammy Awards came to network television close to 40 years ago."
Cossette is survived by two sons, John and Andrew.