The musician's death was confirmed by a statement via his representative, who said that Kristofferson died "peacefully" at his home in Maui, in Hawaii over the weekend.
"We're all so blessed for our time with him," a family statement added. "Thank you for loving him all these many years, and when you see a rainbow, know he’s smiling down at us all".
Kristofferson's legacy will live on, having become a key figure in country music in a career spanning six decades, which included winning Grammy Awards for Best Country Song in 1972 with Help Me Make It Through the Night.
Further Grammy wins arrived in 1974 and 1976, following two duets with former spouse Rita Coolidge.
Kristofferson also won a Golden Globe for his role as John Norman Howard alongside Barbara Stresiland's Esther Hoffman in the 1976 remake of A Star Is Born.
Paying tribute to Kristofferson via Instagram, Barbara Streisand said that "I knew he was something special", the first time she saw him perform on stage.
She continued: "Barefoot and strumming his guitar, he seemed like the perfect choice for a script I was developing, which eventually became A Star Is Born".
"In the movie, Kris and I sang the song I’d written for the film’s main love theme, Evergreen", she added. "For my latest concert in 2019 at London’s Hyde Park, I asked Kris to join me on-stage to sing our other A Star Is Born duet, Lost Inside Of You".
"He was as charming as ever, and the audience showered him with applause. It was a joy seeing him receive the recognition and love he so richly deserved".
Another star to pay tribute to Kristofferson was US country singer Dolly Parton, with whom she also shared many famous duets with over the years, including 'From Here to the Moon and Back', and 'Put It Off Tomorrow'.
"What a great loss", Parton wrote on Instagram. "What a great writer. What a great actor. What a great friend. I will always love you, Dolly".
US singer LeAnn Rimes also called Kristofferson as "an epic human with the biggest heart", while chief executive of Country Music Hall of Fame, Kyle Young also added that the singer, "believed creativity is God-given, and those who ignore such a gift are doomed to unhappiness".
"He preached that a life of the mind gives voice to the soul, and his work gave voice not only to his soul but to ours. He leaves a resounding legacy", he added.
Kris Kristofferson was inducted into the Country Music Hall of Fame in 2004.
He is survived by his wife Lisa, his eight children and seven grandchildren.
