Politely decline an offer that I sort-of accepted I applied to several post-grad programs at Australian Universities. I got an offer from one (University A) very quickly, conditional on completion of my undergraduate degree. It had a lapse date of January 1. During the Christmas break I emailed University A letting them know that I had completed my undergraduate degree but would not be able to get a transcript to them before January 1. I said "Is there anything I can send in the meantime [while waiting for official transcript] that would be sufficient to prove I have met the conditions of the offer and can accept it?" Since then I got another offer from a different university (University B) that suits me better and I plan to accept this offer. 

Today (January 6) I finally got a reply from University A saying "I can confirm you have successfully accepted your offer...". I realize I may have implied that I was going to accept the offer in my email, but the situation changed and I no longer want to accept the offer from University A, since University B is a much better option for me for various reasons.

How can I professionally and politely decline the offer to University A?
Dear [name],
  
  Thank you for your reply to my email of December [xx]. Please note that in that email I asked what documentation I need to send in the event that I decide to accept the offer to join your graduate program, but did not yet indicate a definite wish to accept the offer. In the meantime, I have considered the matter some more and decided to pursue other opportunities elsewhere. Thank you again for the generous offer, for which I am  grateful.
  
  Sincerely,
  
  [your name]