moving site in sub directory to root on same server

I have installed wordpress in my current server, which host my html site. To keep them sepate i have keep installed wordpress in different folder in public_html

public_html (migrate.com) - contain all html files
public_html (migrate.com/wordpress) - contains my new no index site

general settings are:-
WordPress Address (URL) - migrate.com/wordpress
Site Address (URL) - migrate.com/wordpress

Now as the site is all finished . I want o move my new wordpress site to replace the html site. Please suggest the steps to perform it carefully. Thank You