I have to confess that before I came across the construct approve of him I didn't know it even existed. The only version I knew was approve him.
Studying the approve's definitions in the dictionaries cited in The Free Dictionary I concluded that approve someone or something has to do with the transitive use of the mentioned verb whereas approve of someone or something is related to its intransitive use.
The usage note of approve of, according to Collins COBUILD English Usage states:
Don't say that you approve to someone or something.
My question is why? Would you please let me know this?
In rest I think I understand why it's OK to say:
Stefan approved of the whole affair.
The directors quickly approved of the new deal.
Is not OK. That's because using of in this sentence, the sentence will get the first meaning which is not appropriate in this context.