On your extarnal database create a wordpress user, database and set a password.

mysql -u root -p

CONNECT mysql
CREATE DATABASE wp_db_name;
GRANT ALL PRIVILEGES ON wp_db_name.* TO 'wpuser'@'localhost' IDENTIFIED BY 'wp_password';
GRANT ALL PRIVILEGES ON wp_db_name.* TO 'wpuser'@'wordpress_ip' IDENTIFIED BY 'wp_password';
FLUSH PRIVILEGES;
exit