hard coded ip address

Goodmorning everyone,
This will be my first post as I am new to WordPress and to this forum. If I forget to post default information then I am sorry for that. Here is my first question please help me out on this one.

I recently noticed that a website that we host using WordPress has links to the old website which will be down anytime soon. So for example:
My webserver = web01.domain.com
Old webserver = web01.previoushoster.com

The links in my sql database ( phpmyadmin ) are still to the old domain. So all the picture will be loaded from the old webserver. This is obviously wrong. I thought well why not opening all pages and change it manually until I found out it where 1400 links…..
Dohhh :-X

So what I did was exporting the sql database and opened it in a text editor and find replace everything.

However, this is very highly to not work due to user error….

I already read some Sql injections which could be used in phpmyadmin to change it or in function.php

Can anyone please explain me in layman terms of how to achieve my goal as the internet is talking in more advanced form.