How to whitelist all connections in MySQL
This should be easily achieved by issuing the command:

GRANT ALL ON *.* to user@'%'; -- you can also use dbname.* to restrict their 
                              -- access to a given database.


as explained here and here.

You can do some restricting (normally a good idea) by making use of the wildcard (% is the MySQL wildcard) - you can also do '%.domain.com' or '%.123.123.123' or similar if necessary.

You don't have to GRANT ALL PRIVILEGES - you could just give them SELECT and/or UPDATE for example and not INSERT... This is all explained here.