I was able to drive for short trips between weeks 2 & 3 to build up my stamina, and I went back to work exactly 3 weeks post-op. My journey to work takes about an hour and a half, so I needed to try shorter trips first before attempting the big one.
For my first week back at work (Week 3) I had to take paracetamol before each trip, but from Week 4 onwards I haven't touched any painkillers at all. My surgeon recommended that I should wear the surgical binder for extra support whilst driving until I felt I no longer needed it; I stopped using it during Week 4.
It might be worth mentioning that your car insurers might not cover you until you're completely clear of anaesthetic. For me, I felt fuzzy-headed until halfway through Week 2 so I didn't feel safe to drive before that point. My insurers would've refused any claims if I'd driven too soon. If in doubt, call your insurers and ask them what their policy is for driving post-anaesthetic.
I should also point out that I was lucky to have unusually good mobility post-op, but most patients are more limited in their arm movements.
