Time Warner Inc.’s Warner Bros. has agreed to acquire DramaFever, an online video company that specializes in Korean television shows and movies, from SoftBank Group Corp.

Terms of the sale weren’t disclosed. But a person familiar with the matter said Warner Bros. paid less than Japan’s SoftBank did when it acquired DramaFever for $100 million in 2014.

Launched in 2009 and based in New York, DramaFever caters primarily to younger viewers, particularly teenage girls, and has both a subscription and an ad-supported service. While the streaming company is known for subtitled Korean soap operas, its audience is actually broad because that genre has a cult following that spans many cultures.

DramaFever also has a separate business providing technology for other online video services including AMC Network’s Shudder. AMC was among the investors in DramaFever who were previously bought out with SoftBank’s purchase.

The acquisition is part of a broader online video strategy for Warner Bros. parent Time Warner. In August, Time Warner’s Turner Broacdcasting, home of CNN, TBS, TNT and other cable channels, bought a majority stake in streaming video operator iStreamPlanet for nearly $200 million. Time Warner has also recently debated investing in Hulu, the online video service co-owned by Walt Disney Co., 21st Century Fox and Comcast Corp. Last year, HBO launched its own online streaming service called HBO Now.

“There is a great deal of coherence across Time Warner in how we are thinking about the need to reach our audiences more directly,” said Craig Hunegs, president of business and strategy for the Warner Bros. Television Group.

Mr. Hunegs said the first priority is to grow DramaFever, which also carries content from other countries. However, he anticipates eventually launching additional channels. “They have technology and experience in building over-the-top services,” he said, adding “we think there is room for other programming.”

DramaFever will be wholly owned by Warner Bros. In July, The Wall Street Journal reported that Warner Bros. was among bidders for the streaming company, but at the time SoftBank was seeking to retain a significant minority stake in the company, people familiar with the matter said.

The deal is expected to close in the second quarter.

Write to Joe Flint at joe.flint@wsj.com