WordPress.com provides wordpress hosting. But they are not like traditional web hosting provider. Migrating existing website to wordpress.com is little trickier.
Recently we got a client who chose wordpress.com as their new web hosting company. wp engine was their old web hosting provider.
To migrate to wordpress.com, login to dashboard using temporary url. Then go to hosting configuration. There you will find sftp login information and phpmyadmin access.
Open the phpmyadmin, delete all existing tables. Before deleing keep a backup.
Then login to sftp, enter into wp-content folder, rename plugins, themes and uploads directory. Upload themes, plugins and uploads folder you backed up from wp engine.
Now point your domain to wordpress.com
That will make your site live.