Should a postdoc talk about his depression with his mentor?
I'm a tenured faculty member with chronic depression. Even though one of the flareups was in my early twenties, I didn't tell anyone in graduate school. Because of the stigma involved, I'm  unsure even now whether I would advise telling your advisor about this unless you were absolute sure that he would be receptive. The worst case is that he could view you as less than capable and won't push you when he should. Even now (when I'm relatively open about this), I have  used the gloss of personal or family issues when going through particularly difficult times.

But you should also not struggle alone. Your school should have mental health services. There may also be an ombudsman for student affairs. You may also find many of your peers also have mental health concerns. Create a strong support network for yourself.

I also agree with one of the commenters that depression is a chronic condition. I've had several severe bouts through my 20 year career -- and moments when the sun came out and everything felt great. I no longer hold the illusion that any sunny period will last and that I'm free of depression forever. The OP should also plan on what they will do if their depression is chronic, pharma-resistant, or remitting.  That being said, I believe that some aspects of academia are good for people with depression (flexible schedules and being able to work from home for some of us) although there are obviously a lot of negatives as well (toxicity in some departments, incessant deadlines, stress before tenure, contingent employment etc.).