UPDATE: I’m told the trio will stick around for a few months to help out with the transition. But to what? First priority is finding a replacement for CEO Miller.

Miller announced the deal in a short blog post today.

Last.fm, which provides free, ad-supported music streamed over the Web, was the first major acquisition the broadcaster made after bringing on digital M&A pro Quincy Smith, who is making plans to set up shop on his own. CBS (CBS) sends out a steady flow of press releases touting the site’s growth–the most recent one I have, from last month, pegs its audience at 30 million monthly users, while Miller’s post says they’re up to 37.3 million–but turning online eyeballs and ears into dollars has been hard for every Web music start-up, and Last.fm is no exception.

The unit saw its headcount cut significantly during CBS’s reorg of its interactive group late last year, and last month the company combined Last.fm with the online stations from its CBS radio unit.

Here’s text of the post announcing the founders’ departure:

After two years running Last.fm within CBS we feel the time is right to begin the process of handing over the reins. This is the latest stage in a long journey for us founders, which began in a living room in East London in 2002, and took us to the headquarters of one of the biggest media companies in the world.

It’s been a privilege working with the incredible team here in our London office, and we’re extremely proud of what we’ve achieved together. Last.fm’s users have more than doubled in the last 12 months (we are now at an all-time high of 37.3M monthly unique visitors), and we’re confident the site will continue to go from strength to strength. Being a part of CBS, and the recently formed CBSi music group, continues to open up many opportunities for Last.fm. Recent product releases such as the new visual radio, and the Last.fm on XBox announcement, are an indication of how much more Last.fm will achieve.

A huge “Thank You!” has to be said to all of you in front of your computers. With your contribution, enthusiasm and scrobbles you have helped to make Last.fm into what it is today: the best place for music online. Big up yourself for that, as we say here in East London.

That’s all folks, we are going to miss you!

Announcing the debut of Last.fm’s “unprecedented” on-demand music streaming platform, Jones–in a moment of Zuckerbergian grandiosity–proclaimed:

Today we’re redesigning the music economy.”

Which will no doubt come as a bit of a surprise to Apple, and Real, and Amazon and, above all, Imeem, which announced a similar ad-supported service last month.

To be fair, Last.fm’s free on-demand service seems a bit more compelling. Certainly, the CBS-owned site is the only one among the few to offer access to music from all four major labels and a host of independents to anyone willing to stare at an ad for while. And providing complete album streams on a “try before you buy” basis is truly a nice touch.

Still, Last.fm does have one significant limitation: You can listen to a track no more than three times unless you agree to pay for the subscription version of the service or purchase it from an affiliate. Will that be a deal-breaker for the average music fan or a good reason to buy your music through Last.fm, rather than iTunes? Hard to say. “The free-music-on-demand field has been a tough one, with many announcements but few real entries (consider, for example, the often-delayed Qtrax and vaporous Mashboxx),” notes the Los Angeles Times’s Jon Healey. “With CBS’ backing, Last.fm might be able to search longer for a workable formula than the typical start-up. But at some point, it has to find a way to pay the bills.”