He also performed on classic albums such as George Harrison’s All Things Must Pass.
"During the last two years, I had to step away to protect my heart," the singer wrote.
The two bandmates were friends for nearly 60 years.
The flugelhorn player scored a number of entries on the Billboard charts in his lifetime.
The Black Sabbath frontman died at the age of 76 on Tuesday (July 22).
Kaye worked on the singing competition show for 15 seasons.
The star kept his illness private up until his death.
The matriarch made a cameo on her granddaughter's "Ordinary Things."
"Nothing but love and a lovely lasting debt from all of us over here on E Street," wrote The Boss.
The "Real American" singer died on Memorial Day with his wife and caretaker by his side.
