"Very well, thank you"
Welcome to the forum. The dictionary and translator here work very well for phrases like this.
'Very well, thank you' is correct in many cases, however there is an alternative reading of the phrase that might be more appropriate, depending on the context.
If one is asked ¿Cómo estás? - how are you?, the answer 'muy bien, gracias' would indeed mean 'very well, thank you'.
If however you buy something in a shop (for example) and say 'gracias' when given your change, the cashier could say 'muy bien, gracias'. This could be translated into English as 'very well, thank you' but nobody really says 'very well' in this context any more. It sounds very formal.
A better translation (or perhaps interpretation) in this context would be 'you're welcome, thank you'.