Yes. A simple way to confirm is to check out the new bands on Apple's website. If they are Series 3 specific, it will tell you if they were compatible with the earlier versions. They'll all fit fine.
This is one of the things I like about Apple Watch. All four iterations (1st gen / Series 1, 2, and 3) are practically identical in size and thus retain the same band compatibility.
Yes, the bands are compatible across generation. It's wonderful Apple did this - it would have been a huge mistake (and slap in the face to customers of previous models) had they changed the adapter.
Awesome thanks. I ordered a custom band like 2 years ago but never ended up getting an apple watch. I think I am going to get a 3 now that it can basically replace your phone when needed and was hoping the band would still work, sounds like it will.