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 mhan@newserver.com:~/files/
or
$ scp dbs.sql mhan@newserver.com:~/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 dumped SQL file.
$ mysql -u root -p < ~/files/dbs.sql