In short, YES!
If you have old Apple Watch bands laying around, you're just in luck. You will be able to switch them out with the new Apple Watch Series 4.
The new Apple Watch 4 comes in all new sizes, 40mm & 44mm. The 40mm & 44mm is referring to the watch face size and although this years Apple Watch is slightly bigger than the previous models, the old watch band sizes will still fit.
The 38mm bands will fit the same as the 40mm bands and the 42mm bands will fit the same as the new 44mm bands.
This is the first time Apple has increased the screen size for the Apple Watch 4 while still keeping the size of the smartwatch relatively the same size as the previous model. They were able to accomplish this by reducing the bezel around the watch.
The Apple Watch Series 4 is slated to go on sale on Friday, September 21. You can pre-order your Apple Watch now.