The so-called celestial jukebox that digital-music dreamers talked about in the 1990s looks a little closer. Early Tuesday morning, Amazon launched a Web-based music service that lets you listen to your songs from Internet-connected computers and Android smartphones.

Amazon's Android program playing a song stored in its Cloud Player service. (Rob Pegoraro)

Called Cloud Player, it lets Amazon’s “Cloud Drive” servers take the place of a computer’s hard drive or a phone’s flash storage--provided either device has a sufficiently fast connection to the Internet and a user whose Amazon account includes a valid U.S. billing address.

The Seattle retailer provides 5 gigabytes of storage for free; buying an MP3 album from its store upgrades that quota to 20 GB. You can sync new Amazon purchases to your Cloud Drive automatically.

But you can also upload other songs from a Mac or Windows computer using Amazon’s MP3 Uploader. Contrary to what that name suggests, it will also upload AAC files bought from iTunes, provided they’re not older purchases locked with the “digital-rights-management” system Apple retired in April of 2009.

You can then listen to your purchases through a Web browser or on an Android phone running the latest version of Amazon’s MP3 program. A help page on its site suggests that Cloud Player support may be added later to its BlackBerry and Palm webOS apps.

No such option is in store for the iPhone or iPad. Amazon hasn’t even shipped its MP3 store app for Apple’s mobile devices, where it would compete with the iTunes Store and, presumably, be vetoed by Apple.

Based on a quick test Tuesday morning, the whole setup appears stupidly easy. The MP3 Uploader could be a quicker install (the fact that it requires an installation on a Mac at all, by virtue of running on a separate layer of Adobe’s AIR software, earns it a demerit), but it quickly piped a playlist of 22 songs up to my Cloud Drive.

Logging into my Amazon account--whether through the Safari or Firefox browsers or a copy of Amazon’s Android app--then revealed those songs, complete with the correct album art. Amazon says it plays back Web-hosted tracks at their original quality; aside from an occasional blip in playback, that sounds about right. Pausing, resuming playback and skipping to the next song all happened almost as fast as if these MP3s and AACs had been parked on each computer I tested.

In making cloud-based access to your music this simple, Amazon owes a debt to serial music entrepeneuer Michael Robertson. A decade ago, his let users play back songs they already owned over the Web, before major record labels successfully sued to have it shut down.

At the same time, Amazon has also made Apple look foolish and Google appear slow. Apple bought a popular cloud service, Lala, in late 2009 but then shut it down months later; it has yet to introduce any sort of replacement to it. Google, meanwhile, demonstrated its own cloud music offering last May and is apparently still working on it.

Have you tried out Amazon’s Cloud Player? If so, post your own review in the comments.