Stephen Colbert’s announcement on Thursday night that “The Late Show” was being canceled by CBS stunned the entertainment industry, the public and even his staff.

But the writing had been on the wall for some time.

“The Late Show,” a fixture of the network for over three decades, was racking up losses of tens of millions of dollars a year, and the gap was growing fast, according to two people familiar with the show’s finances. Like other late-night shows before it, “The Late Show” was canceled when the network could not figure how to make the finances work in an entertainment world increasingly dominated by streaming.

So as CBS executives mapped out the schedule and budget for next year, George Cheeks, CBS’s president, decided in recent weeks that the network couldn’t take those losses any more, the two people said. Mr. Colbert learned of the decision on Wednesday night. Shari Redstone, the controlling