The new App Centre is part of the newly-listed Facebook's bid to become an all-encompassing entertainment platform, both online and on mobile.
Sticking with the social approach, the store is intended to "make it easier" for users to find apps that they "can enjoy with friends".
Facebook's 900 million members will be able to access a range of mobile and web apps, including Zynga's Draw Something, Nike+ GPS and fellow social network Pinterest.
New apps include various games, such as Jetpack Joyride, Ghosts of Mistwood and Tom Clancy's Ghost Recon Commander, a spinoff of Ubisoft's popular video game series.
The App Centre is said to only list "high-quality apps", based on feedback from people who use the service, and users can browse the store and get personalised recommendations.
Alongside Facebook's website, the app store is also available on the Facebook apps on Apple iOS and Google Android, as Mark Zuckerberg's firm attempts to better exploit ever-growing mobile usage of its services.
In a blog post announcing the App Centre, Facebook's product manager for games Matt Wyndowe elaborated: "You can send apps you find on your computer to your mobile device using the new 'Send to Mobile' feature.
"If a mobile app requires a download, you'll be sent to install it from the Apple App Store or Google Play."
Wyndowe said that every app in the App Centre has screenshots and a detailed description, allowing users to learn more before installing it.
This, he added, also helps with issues of privacy, a key problem affecting online services and the makers of applications.
"It helps you control your privacy by showing the information an app needs and letting you choose who can see your activity on Facebook," said Wyndowe.
"If you decide you want to use an app, you can get started directly from the App Centre."
The App Centre started rolling out to users in the US yesterday, launching with 600 apps. It will be made available to "everyone" in the "coming weeks", said Facebook.