Terms of the deal weren't revealed.
The Wall Street Journal earlier reported that Time Warner would pay $175 million for the San Francisco-based digital sports media network.
"Bleacher Report is a strategic acquisition that further enhances Turner's portfolio of sports offerings," said David Levy, president of sales, distribution and sports at Turner Broadcasting.
Turner owns cable channels TNT, TBS and CNN and manages sports Web sites such as NBA.com and PGA.com.
Bleacher reaches more than 10 million unique visitors per month and syndicates content to publications including USA Today, Los Angeles Times and The Baltimore Sun.