Netflix Inc. signed a deal with luxury theater-chain iPic Entertainment to simultaneously screen its original movies in theaters the same day that they appear on the streaming service, the latest deal to expand Netflix’s theatrical ambitions.

Netflix movies in the next year will play in iPic theaters in Los Angeles and New York City, with the option of showing at iPic’s 13 other locations or independent theaters. Netflix has shown its movies concurrently in theaters before, but the iPic deal represents its first long-term...