What's the correct way to completely remove a URL from a website/search engine?

I had a website which I decided to completely revamp, not only that, the services I offered have totally changed and I built the new one on WordPress. So it's basically a completely new website on top of my old domain.

The new one is up and running and now, I'm trying to get my head around the cleanup process.

I've been to the Search Console and 'temporarily' removed the URL's - I've also deleted the files from the server.

However, I've also read about making all the old pages 'nofollow'.

So now I'm thinking I may need to re-upload the old files to add 'no-follow' to the meta but I was also thinking, perhaps a better idea would be to create a simple 404 that I can use for each page but then, having something on the URL, doesn't that keep it alive? Afterall, I'm trying to wipe these old pages and URL's from existence.

So my question is, what's the best way to go about this (completely remove a URL/page from a website/search engine)?