Hateley, whose son Mark won 32 international caps for England, was lured to Anfield by legendary Reds manager Bill Shankly in 1967.
Shankly signed Hateley from Chelsea for a club-record fee of £96,000, and he spent just over a year with Liverpool, scoring 28 goals in 56 appearances.
A statement on the Liverpool website read: "Liverpool Football Club was today saddened to learn of the passing of former striker Tony Hateley, aged 72.
"The thoughts of everyone at Liverpool Football Club go out to his family and friends at this sad time."
Hateley also played for Aston Villa, Coventry, Birmingham and Notts County during his career, which ended in 1974.
Grandson Tom, the former Motherwell and Tranmere player, wrote on Twitter: "Very sad to hear my dadda Tony passed away today."
Former England striker Gary Lineker added: "Sorry to hear of the death of Tony Hateley. Played with his son, Mark for England, met Tony. A wonderful football family."