The Wallabies coach quit after his side narrowly lost 28-29 on Saturday.
McKenzie told reporters after the game: "I resigned this morning at 10 o'clock. I wrote to Bill [Pulver] and the board members and discussed what's been going on.
"I've been a very proud contributor to Australian rugby. There's a bunch of reasons that I've put in writing to Bill.
"My intention was to resign win lose of draw. I've only just told the team. I didn't advise the team or staff before the game."
McKenzie had been the subject of speculation about his private life and player discontent in the Wallabies camp.