To grant root access from all hosts (except for localhost):

GRANT ALL PRIVILEGES ON *.* TO root@"%" IDENTIFIED BY 'topsecret';

To revoke root access from all hosts (except for localhost):

DELETE FROM mysql.user WHERE User = 'root' AND Host = '%';
FLUSH PRIVILEGES;

To enable MySQL service to accept connections from all hosts change the following line in file mysql.conf:
bind-address=127.0.0.1
to
bind-address=0.0.0.0
or better just comment out:
#bind-address=127.0.0.1
and restart the MySQL service.

Notes:
*) The percent symbol ("%") in the notation root@"%" means “any host”, but it doesn’t imply localhost. You need to repeat the commands above with root@localhost in order to grant/revoke permissions for localhost.