I don't think I'd heard 'I'm good' until I went to NZ 12 years ago. It has spread quickly. Strictly speaking, 'Very well thank you' is the reply to 'How do you do?' which would be grammatically correct as it demands an adverbial answer. If someone says, 'How are you?' grammatically it demands an adjectival answer, so people used to say, 'Fine, thank you', whereas now many, especially the young, would say, 'I'm good' which, as Greatnan says, is grammatically correct, but tends to make me think the speaker is aiming for sainthood.