Buffett, known for the hit song Margaritaville, died “surrounded by his family, friends, music and dogs” at the age of 76 on Friday.
He earned two Grammy Award nominations, two Academy of Country Music Awards and a Country Music Association Award.
Writing in an Instagram story, British megastar Sir Elton said: “Jimmy Buffett was a unique and treasured entertainer. His fans adored him and he never let them down.
“This is the saddest of news. A lovely man gone way too soon. Condolences to (his wife) Jane and the family from (my husband) David (Furnish) and me.”
Sir Elton released a 2006 record called The Captain And The Kid, the same title as a song on Buffett’s 1970 debut record, Down To Earth.
Released in 1977, Margaritaville - taking its name from the popular cocktail - is about having a laid-back lifestyle in a tropical tourist location.
The chart-topping song, which was inducted into the Grammy Hall of Fame in 2016, also lent its name to Buffett’s chain of shops, restaurants and resorts along with a radio station.
Announcing his death on Saturday, Buffett’s Instagram said: “Jimmy passed away peacefully on the night of September 1 surrounded by his family, friends, music and dogs.
“He lived his life like a song till the very last breath and will be missed beyond measure by so many.”
The singer and businessman is survived by his wife Jane, daughters Savannah and Sarah, and son Cameron.