He wrote the letter as part of a publicity drive for the Teaching Awards, which rewards excellence in teaching.
His former teacher, Danny Montgomery, worked at Robert Gordon's College, a private school in Aberdeen. Mr Gove admits that he and his pals had regarded the young and inexperienced teacher as a 'rookie' and 'ripe for ragging'.
In his letter, which is published in the Radio Times, Mr Gove wrote:
"You were, without any pretension or pomposity, attempting to coax a group of hormonal lads to look beyond familiar horizons and venture further.
"And all we could do was compete to think of clever-dick questions to embarrass you and indulge in pathetic showing-off at your expense.'
"You wanted us to enjoy some of the pleasure you had found in the very best that had been thought and written. But we were a cocksure crew of precociously assertive boys who recognised you were only a few years older – a rookie in the classroom – and therefore ripe for ragging. And because we misbehaved, we missed out.
"But because you cared, you persevered. And for that you deserve my apology. And my thanks.
"So Danny, it may be too late to say I'm sorry. But, as my mum told me, it's never too late to set the record straight.'
Mr Montgomery, now 55, still teaches at Robert Gordon's College and said that he remembered Michael.
"Even in those days, Michael stood out," he said, "I remember the words of one of my colleagues at the time: 'That boy is a future leader of the Conservative Party'. He was already known for his sharp wit, strongly held beliefs backed by apparently limitless general knowledge and keen debating skills, which resulted in the downfall of many opponents."
He said it was 'gratifying' that Michael, 45, could recall his lessons.
"It's often hard to know how much is genuinely being communicated in a classroom, so it was highly gratifying to learn that Michael not only remembers the content of my lessons but also appreciates the wider learning that I was aiming to encourage," he said.
Would you want to apologise to a teacher and for what?