The online network was founded in the UK five years ago and it now has more than 15 million active users.
It allows users to connect with other listeners with similar music tastes, to custom-build their own radio stations and to watch music video-clips.
Last.fm founding member Martin Stiksel said it was an "exciting opportunity".
As part of the deal, Last.fm's managing team will remain in place and the site will maintain its own separate identity.
Mr Stiksel said: "This move will really support us to get every track ever recorded and every music video ever made onto Last.fm.
"With a strong partner like CBS, this is now within our reach."
Dot.com boom
CBS Corporation has business interests in TV, web and radio.
CBS radio is the largest radio group in the United States, with 179 stations in the top 50 markets covering news, rock, country and urban music.
The firm's president and CEO Leslie Moonves said: "Last.fm is one of the fastest growing online communities out there."
He said Last.fm's strength in building communities around music and syndicating content was "central to CBS".
He added: "Their demographics also play perfectly to CBS's goal to attract younger viewers and listeners across our businesses."
CBS is not the first major player to purchase up-and-coming websites for millions or even billions of dollars, prompting what some have called the second dot.com boom.
In 2005 Rupert Murdoch's News Corp snapped up social networking site MySpace for $580m (£290m). And last year, search engine Google paid $165bn (£82bn) for video site YouTube.
Mr Stiksel said Last.fm would retain an independent identity.
He said CBS was buying "great technology and a very vibrant, active community".
"They want to move from a content company to an audience company giving the audiences control and learning from this and that's why Last.fm was their choice," he added.
Mr Stiksel said he did not think that users would feel disappointed that a mainstream media firm had bought the site.
"When we said revolution we mean that - we put the users in charge. CBS gets this.
"They understand that consuming media is changing, the patterns are changing."
Online network
As part of the acquisition, the Last.fm management team, including founders Felix Miller, Martin Stiksel and Richard Jones, will continue to independently run the online network
Mr Stiksel said the deal proved that Web 2.0 companies did not have to be in the United States to succeed.
"Being in London has helped us; it's the best place to do things with music full stop. It's the place that leads the world."
The three founders will now be among the most successful - and potentially wealthy - Web 2.0 pioneers in the world.
Mr Stiksel said: "The success of the site is the most important thing. With a strong partner we can add the features we always dreamed about."