St John made 425 appearances for the Reds and scored 118 goals as a key member of Bill Shankly’s famous side of the 1960s.
In a statement on Liverpool's website, the St John family said: "It is with a heavy heart that we have to inform you that after a long illness we have lost a husband, father and grandfather.
"He passed away peacefully with his family at his bedside.
"We would like to thank all the staff at Arrowe Park Hospital for their hard work and dedication during these very difficult times.
"The family would be grateful for privacy at this extremely sad time."
St John won two first division titles under Shankly and scored the winning goal in the 1965 FA Cup final.
He also represented Scotland 21 times, scoring nine goals.
After retiring in 1973, St John went on to manage his hometown club Motherwell and also Portsmouth.
But he won a new generation of fans in the 1980s presenting the popular Saturday afternoon football show Saint and Greavsie alongside former Tottenham and England forward Jimmy Greaves.
Former Liverpool defender Jamie Carragher was quick to pay tribute, posting on Twitter: "RIP Ian St John. Another Liverpool Legend sadly passes away. One of the players along with Bill Shankly who made this club what it is today. I'll remember him most on the best football show on tv, The Saint & Greavsie. X"
St John began his career with Motherwell in 1957 and scored 80 goals in 113 league games.
The Scottish Premiership club said: "We are deeply saddened by the passing of Ian St John.
"Our thoughts are with his family and friends at this difficult time."
The Scottish Football Association tweeted: "We are saddened by the passing of former @ScotlandNT international Ian St John.
"Ian won 21 caps for his country, scoring nine times during a career that saw him represent @MotherwellFC and @LFC. The thoughts of everyone at the Scottish FA are with Ian's family and friends."
Liverpool midfielder James Milner said on Twitter: "RIP Ian St John - what a player, what a man. #ynwa #legend"
Former Reds striker Ian Rush added: "RIP Ian St John sleep well legend!! Thoughts and prayers are with your family at this time".
Reds left-back and fellow Scot Andy Robertson wrote on Twitter: "A man of warmth, humour, knowledge, wisdom and joy.
"Scotland and Liverpool has lost a true giant. My love goes to his family. Rest in peace Ian St John."