This is just one of the ways you can move all of the MySQL databases from one server to another. This was tested on Ubuntu 16.04.01 LTS (xenial) distro.
Log in as an admin on MySQL Console and lock the database to allow only read operations.
mysql> flush tables with read lock; mysql> set global read_only = on; mysql> exit
Dump all of the databases into a file.
$ mysqldump --lock-all-tables -u root -p --all-databases > dbs.sql
Copy the dump to the new server. RSYNC is preferred over SCP, especially if the file is large.
$ rsync -tvz --progress dbs.sql email@example.com:~/files/ or $ scp dbs.sql firstname.lastname@example.org:~/files/
The DB can be (optionally) unlocked. This may or may not be a good thing to do in your case. Do it at your own risk.
mysql> set global read_only = off; mysql> unlock tables; mysql> exit
On the new server, execute this command to import the new SQL dump.
$ mysql -u root -p < ~/files/dbs.sql
IMPORTANT: If your file is large, or you just have a lot of records, you may want to make sure you have something bigger than 16M for max_allowed_packet attribute in your my.cnf (usually found under /etc/mysql/ or /etc/mysql/mysql.conf.d/) on your new server where you’re doing the import, else the server could hang on a large insert operation and your MySQL server may actually decide to go away, literally. On one of the servers I had it for 1024M just for this operation and brought it back low afterwards.