Spurs secretary Alexander will take up the same position at Manchester United when Ken Ramsden retires at the end of the season.
He will become only United's fifth post-war secretary when Ramsden ends his three-year tenure in May.
Alexander said: "I am honoured to be offered the chance to be the secretary at the world's biggest football club. I have a series of very hard acts to follow but I am looking forward to working with (manager) Sir Alex (Ferguson), (chief executive) David Gill and the team."
Gill added: "John is the perfect candidate to succeed Ken. He is a real football man with a wealth of experience in the game."