His website quoted his wife, Jan Bridges, as saying that he died in his sleep at his Nashville home.
No cause of death was given on his official website and Facebook page but the singer, songwriter and musician had suffered a heart attack in July and underwent bypass surgery.
Over his nearly six-decade career, Russell, a member of the Rock and Roll and Songwriters Halls of Fame, performed, toured and recorded with a wide-ranging roster of performers.
Other notable songs written or performed by Russell include "This Masquerade," a hit for George Benson," and "Superstar," made famous by the Carpenters.
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Russell performed at the Concert for Bangladesh with George Harrison and Friends and toured with acts including Delaney & Bonnie and Friends, Edgar Winter, the New Grass Revival, Willie Nelson, and Elton John.
During the 1980s and 90s, he played country music under the name Hank Wilson but returned to the spotlight when he recorded "The Union" with Elton John in 2010.
Russell was born on April 2, 1942. He began learning piano at the age of four; by his early teens, he was playing in Tulsa nightclubs.
Following his graduation, Russell toured with Jerry Lee Lewis for a few months, then moved to Los Angeles and found work as a session musician.
As a solo artist, Russell's most successful years came in the 1970s, beginning with his eponymous solo debut in 1970 and subsequent releases 'Leon Russell and the Shelter People and Carney.'
Musicians took to social media to express their condolences.
Elton John called Russell a "mentor" and "inspiration."
"My darling Leon Russell passed away last night. He was a mentor, inspiration & so kind to me. I loved him and always will #LeonRussell #RIP"
"Another musical giant leaves us today. Thank you. What a week. RIP #LeonRussell," wrote Nils Lofgren.
Yusuf / Cat Stevens tweeted, "So sad to hear Leon Russell has passed away. A great influence and songwriter. God rest his soul."
"The magnificent Leon Russell amazing musician, true superstar "Long ago and so far away,I fell in love with you..After the 2nd show" RIP," wrote Whoopi Goldberg.