Always backup your MySQL database with mysqldump but if you didn’t you can restore it from file system.

If your backup include the /var/lib/mysql directory, if so then you should be able to restore the database. Each database is contained in a separate subdirectory off /var/lib/mysql, so look for one named with the name of your database (WordPress or any other). To restore it, shutdown the mysql server first

sudo /etc/init.d/mysql stop

Copy the backup-ed directory into the same location on your new server, then restart mysql server

sudo /etc/init.d/mysql start

Note:- that its much better to take actual database dumps using the mysqldump command than to rely on this method. so for the future, you should schedule something like this:

mysqldump -h host -u user -ppassword --databases database1 database2 > myfile.dump