The free-to-play tactical game, which is developed by Kabam, is based on Peter Jackson's movie trilogy.
Featuring characters such as Bilbo Baggins, Thorin Oakenshield and Radagast the wizard, players are tasked with leading an army of elves, dwarves or orcs into combat.
Described as a "deep and immersive strategy game", players can build an empire in Middle-earth and join forces with other players online to wage war.
Warner Bros Interactive's Greg Ballard said that Facebook is the perfect place to engage with Tolkien film fans.
"The Facebook and browser-based portals are key locations where The Lord of the Rings and The Hobbit film fans can regularly engage with Middle-earth in a shared interactive environment," said Ballard.
Kabam and Warner Bros Interactive previously partnered for iOS and Android game The Hobbit: Kingdoms of Middle-earth.
"The Hobbit: Armies of the Third Age and The Hobbit: Kingdoms of Middle-earth deliver two immersive and dramatically different ways to experience the most iconic fantasy world of all time, across the Web and mobile devices," said Kabam's Andrew Sheppard.
The Hobbit: Armies of the Third Age is also playable on Kabam's website and through the Google Chrome store.
It was announced last year that The Hobbit will be split into three films, rather than two as was originally planned, and the next two films will be released in December 2013 and 2014.
The second film in the trilogy, The Hobbit: The Desolation of Smaug, is released in cinemas on December 13.
Watch a trailer for The Hobbit: An Unexpected Journey below: