Netflix NFLX -4.19% and Amazon’s battle for India’s streamers is heating up.

Netflix said Thursday it has hitched up with one of India’s most popular film stars, Shah Rukh Khan, a day after Amazon launched its video service globally and announced a robust slate of Indian original series.

As part of the deal, Netflix will exclusively stream all new films starring Mr. Khan worldwide, the beginning of a “long-term relationship” between the streaming juggernaut and Mr. Khan’s production company Red Chillies Entertainment, the companies said in a statement.

The deal gives Netflix subscribers access to “dozens” of Mr. Khan’s library films as well as his new films coming to Indian theaters over the next three years. The first title coming to Netflix is “Dear Zindagi,” which will be released in theaters Nov. 25.

“Shah Rukh Khan is the most sought-after actor in the Indian film industry, and has played a huge role in bringing Indian cinema to the world stage,” said Netflix Chief Content Officer Ted Sarandos in the statement. Netflix also released a YouTube video teasing the deal with “King Khan.”

“Red Chillies is surging ahead in global entertainment and for the first time, our great stories are going global on Netflix all at once and crossing all geographical barriers, waiting to be discovered over the world,” Mr. Khan said in the statement. “No more waiting for our fans.”

India is shaping up to be an important market for Netflix and Amazon, especially since neither have figured out how to break into China due to its tough regulatory regime. Though a small portion of India’s 1.3 billion people have internet access, it has 18 million broadband homes and 149 million mobile broadband subscribers.

Amazon is also aggressively courting big-name Bollywood players as it beefs up its library in India, but unlike Netflix, it is willing to take a bet on regional content that may not “travel” in its other territories.

Yesterday, Amazon announced nine original Indian series with well-known Indian producers, including Ram Madhvani, as well as local-language kids’ series, library film deals with the likes of Yash Raj Films and regional movies in Tamil, Telugu, Bengali and Marathi.

Netflix’s announcement with Mr. Khan exemplifies its choosier approach to lock up local deals that could have global appeal, similar to its deal to produce its first Indian original series based on the internationally-acclaimed Mumbai crime novel “Sacred Games.”

Still, in the wake of Amazon’s video launch worldwide, the arms race between the two to link up with local stars whose work can travel will only intensify.

Write to Shalini Ramachandran at shalini.ramachandran@wsj.com