Honesty is definitely the best policy but first you need to realise there is often a big disconnect between what an advert says, what HR described and what the Hiring Manager really wants!
You need to find out if the person who interviewed you is the Hiring Manager. If so, then it's quite likely that they're struggling to fill the role and think you can, at the very minimum, grow into it.
So pick up the phone, speak to HR and tell them that you are delighted to have been offered this position even though you applied for a different one and you just wanted to double check they understood the situation. Don't be bashful or apologetic though - you spent an hour impressing a hiring manager on a subject that wasn't expected to be your main focus!
"I'm really excited to be offered this role, I think I can do a great job for you and the interview seemed to go well but I just want to double check with you as the job I was offered wasn't the one I applied for. I don't have a problem with that but just wanted to double check it's all OK at your end."
