GRANT ALL PRIVILEGES ON *.* TO 'root'@'%' IDENTIFIED BY ('myrootpassword');
* EDIT * : The above statement does not necessarily copy all privileges over to the new entry for 'root'@'%' in the mysql.user table. A better way to accomplish full external root access is the following :
DELETE FROM `mysql`.`user` WHERE User = 'root' AND Host = '%';
INSERT INTO `mysql`.`user` (Host, User, Password, Select_priv, Insert_priv, Update_priv, Delete_priv, Create_priv, Drop_priv, Reload_priv, Shutdown_priv, Process_priv, File_priv, Grant_priv, References_priv, Index_priv, Alter_priv, Show_db_priv, Super_priv, Create_tmp_table_priv, Lock_tables_priv, Execute_priv, Repl_slave_priv, Repl_client_priv, Create_view_priv, Show_view_priv, Create_routine_priv, Alter_routine_priv, Create_user_priv, ssl_type, ssl_cipher, x509_issuer, x509_subject, max_questions, max_updates, max_connections, max_user_connections) (SELECT '%', User, Password, Select_priv, Insert_priv, Update_priv, Delete_priv, Create_priv, Drop_priv, Reload_priv, Shutdown_priv, Process_priv, File_priv, Grant_priv, References_priv, Index_priv, Alter_priv, Show_db_priv, Super_priv, Create_tmp_table_priv, Lock_tables_priv, Execute_priv, Repl_slave_priv, Repl_client_priv, Create_view_priv, Show_view_priv, Create_routine_priv, Alter_routine_priv, Create_user_priv, ssl_type, ssl_cipher, x509_issuer, x509_subject, max_questions, max_updates, max_connections, max_user_connections FROM `mysql`.`user` WHERE User = 'root' AND Host = 'localhost');
FLUSH PRIVILEGES;