Back In Feb this year, WordPress.com launched "Publicize" for Facebook, which automatically shares a link to new posts to Facebook account(s). Since, user have been demanding the ability to Publicize to Facebook Pages. Now, today on August 8, the WordPress team announced this support.
If you already have Publicize active, you'll now see a link to set options for Facebook, inside the Facebook block on the Sharing Settings page. If you click on it, you'll see a simple dialog box that lists all your available pages to pick from.
If you are new to Publicize, you'll see a sequence of screens confirming permission to post to your Facebook account, before you see the screens, see pic(s) below.
Also note, "currently you can only Publicize to one target: either a page or your wall. This should be more than sufficient to get your great posts out to a wide audience of your choosing," the WordPress team added.