Took me a few months. I immediately dropped down to 2-3 smokes a day (first thing in the AM with my coffee, right after a big dinner, sometimes right before bed); figured I needed those three to function normally and every other cigarette I smoked throughout the day was more or less an excuse for a quick break that I could replace with vaping.
After a week or so, my smoking just kind of naturally dropped to one a day, then one every few days, then none at all. I still bought a pack maybe every couple of months or so if I felt like smoking, but I was always able to go back to full-time vaping pretty easily. Last pack I bought was probably around a year ago, I still have most of that pack left, sitting in my closet.
I think the biggest thing for me was that I allowed myself to have a smoke if I wanted to (still do, actually, although I can't remember the last time I did). Most of the other times I tried to quit (gum, patches, etc.), as soon as I had a single cigarette I felt like I failed, and I was right back on the wagon. Since I allowed myself to have a cigarette if I really wanted one, smoking one or two on a night out or whatever didn't feel like a big failure.