Moving WordPress

Hi
I recently moved my domains to new web hosts.
I still have access to the old WordPress files and database through ftp and phpmyadmin, not through a web browser.

In order to move sites do i just export the database, import to new hosts and upload all the exiting WordPress files?

I tried using Backwpup 2.1.9 but it never works during the restore.
So within the Backpup files i already have the .sql and all the WordPress files.

Tried a few times now and I’m getting lost :-/

Is there anything i can do or do i have start a fresh?

Thank you

Jonathan