Hateley scored 211 league goals during his career and was a club-record signing for both Chelsea and Liverpool, costing the Blues £100,000 in 1966.
His son Mark was also a striker, playing 32 times for England.
A Liverpool statement said: "The thoughts of everyone at Liverpool Football Club go out to his family and friends at this sad time."
Hateley started his career with Notts County before moving to Villa Park in 1963, scoring 68 times in 127 league appearances.
After his big-money move to Chelsea, Liverpool paid £96,000 to take him to Anfield and at the time of his retirement in 1974 his combined transfer fees were a record in English football.
Match of the Day presenter Gary Lineker tweeted: "Sorry to hear of the death of Tony Hateley.
"I played with his son, Mark for England, and met Tony. A wonderful football family. #RIP."
Son Mark was prolific at Portsmouth, AC Milan, Monaco and Rangers during the 1980s and 1990s and grandson Tom Hateley is also a professional footballer, currently playing in Poland after spells at Motherwell and Tranmere.