Greaves' record as the highest-scoring Englishman stood for six decades until Kane overtook his tally two months ago.
Kane left the Premier League as the second-highest scorer in the competition, with Alan Shearer holding the record with 260 goals.
According to the International Federation of Football History & Statistics (IFFHS), Shearer sits fourth in the all-time list of English scorers with 409 goals, with Steve Bloomer - who played in the early part of the 20th century - third with 412 goals, behind Greaves and Kane.
Dixie Dean sits fifth with 396 top-level goals and Rooney is sixth on 360.