Microsoft has already released an iPhone version in June.
Microsoft is also offering Office programs in tablets running its own Windows system.
Microsoft said it designed Office Mobile for Android phones specifically for small-screen devices. The company has a version for iPads and Android tablets, called Office Web Apps, but that runs on a Web browser and requires an online connection. The new Android software is an app that gets installed on the phone and can work offline.
With a subscription, Microsoft's customers get to use Office on up to 10 devices. Five of them can be Windows or Mac computers or Windows tablets. The other five can be iPhones or Android phones.
The new software requires Android 4.0 or later. It's available through Google's online Play store.