Make sure the new site works and no errors. If you just registered a new domain, the resource can remain unavailable for some time. Continue the process of transferring your data, since the page will open after you change the name of the DNS server.
What is the process of transferring a site
Delete the entire folder and content of the new site. Copy the entire contents of the old resource with the new one. It will include all the themes, plugins and downloadable content (media, for example). You can do it any way you like, for example, to create an archive of the content from old site and use Cpanel to download it to your computer, then upload to the new site and unpack. Another way is using FTP to download your old content and re-embed.
Importing database to new domain
Open the DB Admin page. Enter the name of the new website and the full path where it is placed. Save the database from your old resource on your computer.
Open Manager MySQL database on the new site (PHPMyAdmin, most likely). Select the database name used for the new site. Select configure the database structure by clicking the option "Check All". This will clear all entries in the database for the new site. Now select the Import tab and browse for the file saved from the old site. Add it to the new database.
Your new site is ready to go and will work under a new name. All links to the content and notes will be available under the new addresses. However, the administrator and registered users can log in under the same names and passwords. All plugins and sidebar should function as before. In other words, you completely clone the old site, but it will now operate under a new domain name.
If you move to a new host, you must also update the server names in your account within the domain Manager. It may take a few hours or even a day until the required information is stored.
It is desirable that the old domain for some time was still available. With it, you can inform the visitors of your website, the address is changed, placing on the advertisement page.