James Corden, a onetime comic performer on the London stage who found his niche on American late-night television as the host of “The Late Late Show” on CBS, will continue to hold down the network’s 12:30 a.m. slot for the next few years.

CBS announced on Monday that it had extended Mr. Corden’s contract through 2022.

He hit the airwaves in 2015, a time when the late-night landscape was in the midst of a substantial reordering. David Letterman and Jon Stewart both left their late-night shows in 2015, and Jay Leno had stepped down from “The Tonight Show” in 2014. Mr. Corden replaced Craig Ferguson, who left as host of “The Late Late Show” in 2014.

Five years later, there is stability in late night, and the successors of the departed hosts seem to be in it for the long haul.

Jimmy Fallon, who replaced Mr. Leno as the host of NBC’s “The Tonight Show,” is signed through 2021. Trevor Noah, Mr. Stewart’s replacement at “The Daily Show,” is signed through 2022. At ABC, the host of “Jimmy Kimmel Live,” the longest-serving broadcast late-night show, also recently signed a three-year extension. Stephen Colbert, Mr. Letterman’s replacement on CBS, hosts the most-watched show in all of late night.