Yes. Wave is a website with nothing to install, so it works on Linux the same as on Windows. Wave's own help says its tools are web based and no installation is necessary.
Wave Accounting by Wave Financial · Business & accounting · Works in a browser
Wave never had a Windows program to lose. Everything happens at waveapps.com in a browser, which
means Firefox or Chrome on Linux gets you the identical product. Invoices, bookkeeping, receipts
and reports all behave as before.
Because your data sits on Wave's servers, there is nothing to export and nothing to convert. Sign
in on the new machine and your books are there. That is the quiet advantage of having been on a
cloud service already.
Wave's mobile apps are iOS and Android only, so if you used one of those on a phone, keep using
the phone. There is no Linux desktop app, and you do not need one.
The only thing worth checking is your bank connection. If Wave imports transactions from your bank
automatically that will keep working. If you were downloading files from internet banking and
uploading them by hand, confirm your bank's website behaves in your Linux browser, which it almost
certainly will.
Worth considering only if you want your books on your own machine rather than someone else's server. Free, and more capable than Wave, but harder to learn.
Your files: Imports CSV exports from Wave. Categories will need checking after the import.