To enable the administrator review for a new user account – please use this plugin https://wordpress.org/plugins/eonet-manual-user-approve/
UP 24.11.2020: Since Free version 2.16 this plugin also supported: https://wordpress.org/plugins/new-user-approve/ (but the message appears from the plugin, for now, so not possible to edit it).
Just change the Success registration message from
Registration was successful. We have sent you an email with your login information. Please use them to log into your account.
to something like:
Registration was successful. We have sent you an email with your login information. After admin review and approval you can log-in. You will be notified about the review results by email.