URL change

I’ve built a new WP site on my server and just used a redundant url to point to it.
However the site is now ready to go live and I now want to close an old e107 site down and point its url to the new WP site and make it the default address.

I’ve pointed the url to the wp site but all the internal links are still using the old address I used during the build.

I’ve read what seems like tens of docs on this subject and just got more and more confused as I don’t want to move the site or it’s files anywhere.
I just want to change the sites default url.

(A simple one click process in e107)