Signed from Chelsea for £96,000 in 1967, Hateley spent just over a year at Anfield and scored 28 goals in 56 games.
His son, Mark Hateley, later played for England.
Liverpool announced on their website: "Liverpool Football Club was today saddened to learn of the passing of former striker Tony Hateley, aged 72."
Hateley also represented Aston Villa, Coventry, Birmingham and Notts County during his playing career.
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."