Hunt, who was also part of England's line-up that won the World Cup in 1966, is the Reds' second-highest goalscorer with 285 goals.
Liverpool said in a statement posted on their official Twitter account: "We are mourning the passing of legendary former player Roger Hunt.
"The thoughts of everybody at Liverpool Football Club are with Roger's family and friends at this sad and difficult time. Rest in peace, Sir Roger Hunt 1938 - 2021."
The former striker's passing comes just over a week after the passing of Three Lions teammate Jimmy Greaves.
Tributes have come pouring in for Hunt, including from former players Robbie Fowler and John Aldridge, as well as Reds manager Jurgen Klopp.
"It's really sad news and our thoughts and our love go to his family," Klopp said.
"Unfortunately, it feels too frequent in this moment we are saying farewell to these giants of our club.
"Roger Hunt comes second to no-one in his importance in the history of Liverpool FC, that much is clear.
"To be the goalscoring catalyst of the Bill Shankly team to actually achieve promotion and then go on to win those precious league titles and the FA Cup puts him in a bracket of LFC legends who are responsible for making us the club we are today. Not only that, he was also a World Cup winner in 1966, too.
"I am told the Kop christened him 'Sir Roger' for all his achievements. A goalscorer who never stopped working to help his teammates; I believe he would have fit in well within our current team.
"So, it is Sir Roger we will remember, honour and pay tribute to over the coming days. You'll Never Walk Alone."
Former Liverpool defender Phil Thompson told talkSPORT: "It's another shock for Liverpool fans. Too much of this has happened in the recent past. I stood on the Kop idolising Roger.
"It was no different when I signed for Liverpool as an apprentice in 1969, just going in that dressing room, he was only there for another year but it was great just to be so close to him being a fan.
"They often say in life you should never meet your heroes, but Roger Hunt never disappointed me.
"We were friends as ex-players and it was great being in his company. Full of humility and was an absolute wonderful man.
"As a player, he thrilled the life out of me and Liverpool fans back in the 60s. In the 60s, Liverpool was the centre of the universe. Everton were doing well and Liverpool were doing well.
"Roger and Ian St John, bless him, were just iconic figures. I loved Roger, absolutely loved him. To be that close when I was an apprentice was an absolute joy.
"This is a desperate blow for everybody who supported Liverpool and of course we knighted him."
Hunt was born in Golborne, Cheshire on July 20, 1938.
He signed for Liverpool in July 1958 and made his final appearance for the club in December 1969.
Hunt was signed by Phil Taylor from non-league Stockton Heath but was kept on by Shankly, and helped the club out of the old Second Division in 1962, going on to win league titles in 1964 and 1966.
He also won Liverpool's first ever FA Cup in 1965, scoring in the 2-1 win over Leeds at Wembley.
Hunt won 34 caps for England, scoring 18 goals, and earned his first under Walter Winterbottom in 1962 when Liverpool were still in the second tier.
In that season, he scored 41 goals in as many games for the Reds.
Hunt scored three goals in helping England get out of their group at the 1966 finals, and played in every game such was his importance to Sir Alf Ramsey's team.