How to write a sincere reply to a very positive reply from a professor?

Thank you for your reply, Professor X. I am happy to hear that you're interested in taking on a PhD student for next year, I will definitely be putting in an application for the position. I look forward to hearing more about the project in the future. Regards, me.

You don't need to throw them a parade, but take a little more time to email them something other than just,

Thanks a bunch!

I tend to agree with Eppicurt. Keep it professional.

I suppose there's a fine line between being confident and being flatter. Only you can decide where that is.

Assuming you have heard this person lecture, read their work, and inquired with others as to what it's like to work with Prof X, you could simply write back:

"Thank you for the instruction to submit my application. I am enthusiastic about an opportunity to work with you because...., and I trust you will find my application competitive with the other applicants."

I imagine that Prof X will have the final say on who she or he selects and a professional and courteous email is always welcome.

Best of luck with your application!