Move custom made PHP MySQL system/CMS to new server

I have two custom made CMS:s/systems on a server and would like these to be moved to another server. One of them is a custom made CMS, which used to be used for a web site. The other one is a system made for members to login and share different kind of information. Both are made with PHP and MySQL. I have the FTP details and the details for the database, but what I need is for some programmer to find out what to change in the files/database to be able to move the systems to a new server, so that the sites can be viewed online in a browser, from the new server. I would prefer to send the FTP files as a zip file (ie not be downloaded from the old server) or similar. And the same with the database (I send it as a SQL file rather than spread all the details for the old server). Though you will get the details for the new server's FTP and MySQL and temporary online URL:s.