Connecting Mail Domain With App Database

Hi, Here i need a suggestion for mail domain connecting with app database. In my application have user registration and the registered users can send mails (Site based mail box - uses application database (mysql) ). So users can send mails after logged into this application. Now i want to send mails without user login. My idea is

On registration time - Provide unique mail address for users like - Umail_id@app_name.com

The users can send mail to this mail address from any mail domains like gmail

So i want to connect this unique mail with our application database (Site based mail)

Need suggestions for to implement this.
Thanks.