Probably some driveshaft work, as the 4L60 housing is different length than the TH350 or TH400 that was originally in that car. But I'm almost positive the proper bellhousing will bolt up to a SBC.
You may need to match SBC flexplate bolt pattern to the correct torque converter for the application. Since the 4L60 is based off the TH350, you're probably OK w/ regard to the dimensions of the transmission tunnel in the Impala chassis (e.g.; height / width). I'd still measure beforehand, but you'll prolly have plenty of room. You might have to mod the shift linkage; be prepared for that.
There are resources online that will describe all of this (except for the Impala's tunnel dimensions.) Find at least two different sites that match info before you start searching for parts. There are also some minor variations internally in the 4L60, but most of the bigger changes came in 2005-up. Nothing that should affect you, unless you start modding the trans - then you need to know the vintage (and you do, so you're good).
IIRC,1999-2003 is a breakpoint for 4L60s; before you put the trans in the Impala, grab the ID codes off the trans housing. GM wasn't above putting in older / newer parts in vehicles, depending on what time of year the vehicle was built & what parts were in the bins, etc. So depending on when yours was built, you could have an '03, an '04, or even an '05-spec 4L60 (this would be rare, but if you have a late '04 build (per the driver's door label), it's worth validating).
If that 400 SBC has been built with high HP, consider beefing up the internals on the 4L60; GM built them with more and more plastic parts as time went on. Properly built, they are supposed to be good to about 700HP max.
If the motor is stock, you should be OK with the trans as-is, internally (you already know you need a controller for the trans, as well as a new torque converter & bellhousing). Properly cared for and not abused, a 4L60 can last about 200K or a little longer (although I'd at least put a TransGo corrective shift kit in (orange box) and maybe some metal accumulator pistons in the valve body (in place of the plastic ones) to help get to that 200K).
There are plenty of 4L60s in old F-body cars, as an example, and many of them still have SBCs installed. So it's definitely do-able; you just have a little homework to do. You'll probably need to input the rear diff ratio into the controller programming, I would guess.