old office files on new operating system

Yes, the files are fine. However if you were using a 32 bit version of Office for Mac, you will need to buy Office for Mac 2016 or later (Office for Mac 2019 or subscribe to Office 365) in order to run the apps. Catalina and later versions of Mac OS will only support 64 bit apps so that is why you may need to upgrade your copy of Office for Mac. The first thing to do is check what version you have, y ou can do this in any of the apps (Word, Excel...) in the About ......

How old?

What system is on the new iMac, Big Sur? If so then only MS Office 2019 or MS Office 365 will run. The same holds true with Catalina but MS Office 2016 with the latest software will work on Catalina. Not sure about Big Sur.

However there's a very good alternative which is the free LibreOffice. It can open, edit and save Excel and Word files in MS Office format or their own format. Apple's Pages and Numbers can do the same but not as effectively.

The files aren't 32 bit, only the apps. So the later MS Office apps that are 64 bit or the alternatives I mentioned above can still open them.