Michele, 29, will play Amanda, a witty, type-A girl who finds herself using online dating services as a way to try to get over a bad breakup. She matches with a guy named Adam (Buckley), who makes the mistake of saying "I love you" too soon.
Trophy Wife star Ryan Lee has also been tapped to star in a stand-alone episode set in 1982, playing Andrew, an introverted, bullied teen who is addicted to video games.
The series is inspired by the Internet's "404" code error and will explore the mysteries of the digital age through hour-long episodes. According to a press release for the show, Dimension 404 "aims to evoke that 3 a.m. feeling of wandering onto the weird side of the web, stumbling upon stories that cannot be explained in the world that we know."
Last month, a source told ET that Michele and Buckley, 35, met through mutual friends and have been dating for a couple of months. They are "totally crazy" about each other, the source added.
When ET caught up with the Scream Queens actress at the FOX Upfronts in New York City, she played coy when we asked her to spill all on her new beau.