Should I explain my poor performance during undergrad, due to mental illness, when applying for PhD? I was mentally ill for the first three years of my undergraduate studies (altogether, I had the diagnoses of severe depression and anxiety disorder for about five years). The diseases delayed my progress considerably. However, I recovered, and have done extremely well after that.

Two programs, both top-ten globally, are interested in hiring me. I have not listed my grades on my CV to avoid giving a bad first impression; I have instead highlighted my achievements: publications, prizes, research experience, etc.

How / when should I mention this? My BSc is average and MSc very good. I hope they do not care about the undergrad grades. If there is an "other information" box in the applications, should I state something along the lines


  My performance during my undergraduate studies was not good due to severe illness. However, I have fully recovered, and done very well since


I know there is a previous question about getting a bad transcript past admission committees. However, I think my qualifications are really good without the bad beginning. Also, I would like not to mention I was mentally ill. What to do here?
You do not need to disclose the nature of your illness if you do not wish to.  It was your illness, and you get to decide how you handle it.

The short explanation you propose is fine.  You might want to specify that it was the first three years:


  My performance during the first three years of my undergraduate studies was not representative of my abilities, and was due to illness. However, I am glad to say that I have fully recovered, and as my transcripts show, I was able to overcome those early difficulties.