Bebo, which launched in 2005, has failed to match the huge popularity of sites like Facebook and Twitter.
AOL Inc., which is based in New York, tried to use the site to drive traffic to its other ad-supported Web properties, but it hasn't taken off.
The site had about 5 million users in February, according to comScore Inc., compared with Facebook's 210 million. AOL said in April it planned to shut the site or sell it.
The buyer is the private investment firm Criterion Capital Partners LLC.
The California company did not say how much it is paying, but analysts have speculated that the site would fetch just a fraction of what AOL paid for it.