Alexander also taught Johnson's sister Rachel and said intelligence was in the family's genes.
"The whole family was very clever. He did take advantage of that and made use of his brains," he said.
"Boris was an all-rounder and didn't have any obvious weaknesses. It may seem like hindsight but I did really feel he was a boy who was going places."
Johnson also had charisma in the classroom, Alexander said.
"You knew he was in the room. He was a perfectly pleasant boy to get on with and as far as I remember he was quite popular and got on with his fellows very well."
Alexander said Johnson had a reputation for being a bit of a buffoon but that was his way of getting recognised and liked among voters.
"He is by far no buffoon," he said.
In Alexander's eyes, Johnson impressed as London's previous mayor and had also proved himself in politics as a great Brexit campaigner.
Alexander said he had kept a close eye on the politics back in the UK since moving to New Zealand in 2013.
"I just got the impression he wanted to be Prime Minister, I am quite certain about that. I tipped him very early on as a future Prime Minister."
Alexander had not spoken to Johnson since the pupil-turned-Prime Minister left school.
But when asked what he would do if the Prime Minister knocked on his door tomorrow, Alexander said he would happily invite Johnson in for "a drink and a good chat".
"I would like to see him very much. I think he will do a great job as Prime Minister of the UK."