Is a good idea to inform potential PhD Advisor that I sent my application for joining his lab? I sent an email to a potential PhD advisor few months ago where I expressed my interest to join his lab, he replied to me the next day mentioning to me that he would be happy to apply to the program through he is currently recruiting. 

Yesterday I sent my application. 

Is a good idea to inform him that I sent my application? because I didn't apply directly to him but to the program of the institute he is working and I am a bit nervous.

Thanks in advance!
If that makes you feel better, sending a quick email is probably fine. Something along the lines of:

Hello Dr XXX,
I have just submitted my application to program Y, as you have advised. Looking forward to hearing back from them!
Best,
Student

Even if you don't get a reply, a quick note like this should be sufficient to remind the professor that you are still interested in his lab. Good luck!