The move comes as the Time Warner company continues to try and penetrate a wider, younger audience via streaming and other digital services.
Warner Bros is buying DramaFever from Japan's Softbank, which bought the firm in 2014.
The deal is expected to go through in the second quarter of 2016.
"Warner Bros is truly the ideal home for us," said chief executive and co-founder of DramaFever, Seung Bak, of the deal.
Warner Bros is also pushing into China's lucrative film and entertainment market as it seeks to grow its audience base there. Last year, it teamed up with a Chinese investment firm to develop Chinese language films.
DramaFever is available in more than 20 countries and offers a wide range of shows and films in multiple languages. It was launched in 2009 with  one Korean series and will continue to be based in New York once the deal goes through.
Warner Bros said DramaFever's two founders Seung Bak and Suk Park would continue to oversee the company.
Entertainment giant Warner Bros has agreed to buy DramaFever - a US-based streaming and on-demand service with a focus on Korean shows and movies.