His death was confirmed by Barbados Prime Minister Mia Amor Mottley, who called for a moment of silence for the man who wrote its national anthem.
Mr Burgie is best known for helping singer Harry Belafonte bring calypso music to the mainstream.
The 1950s song Day-O went on to be used in films, adverts and even as a wake-up call for astronauts in space.
The calypso hit, also known as The Banana Boat Song, featured in the popular film Beetlejuice and has been sampled by rapper Lil Wayne and singer Jason Derulo.
US media reports say Mr Burgie died on Friday as a result of complications from heart failure.
His website says his songs have sold more than 100 million records worldwide.
Mr Burgie wrote eight of the 11 songs on Harry Belafonte's 1956 album Calypso, which was the first album in the US to sell more than a million copies.
During his career, the composer worked with artists including Jimmy Buffett, Chuck Berry and Sam Cooke.
His other well-known songs include Island in the Sun, Jamaica Farewell and Mary's Boy Child, which he co-wrote.
Brooklyn-born Mr Burgie did not begin pursuing a career in music until he returned from serving in an all-black US Army battalion in World War Two.
He then used the benefits he received as a war veteran to fund his studies at New York's prestigious Juilliard performing arts school and went on to launch a career as a singer and guitarist before moving into writing songs for others.