Word of David Letterman’s retirement announcement leaked just a few minutes after he shared the news at his “Late Show” taping on Thursday, but the rest of the viewing public had to wait until the program aired Thursday night to find out: Why did Letterman decide to retire after three decades in the late-night TV game?

The short answer: Because that’s a really, really long time, and he’s ready to be done. Longer answer: Buckle up, because Letterman chose quite the roundabout route to share the big news.

First, he gave a preamble rattling off some statistics about his career, kicking things off with the fact that he’ll turn 67 in a few days.

“The only reason I bring this up is when Paul and I started together doing this show — then we used to have another show at another network, over there at NBC — I was 34,” Letterman began. “So if you figure that up, roughly, I have spent half my time behind this desk. More importantly, that means I’ve spent half my life in makeup.”

All together, 4,014 episodes at CBS and 1,810 shows at NBC (including the short-lived morning show) brings the total to 5,914 shows over 34 years. Wondering why he was bringing this up? Letterman told the audience that people have always asked him how long he would continue to host. His answer is usually, “When this show stops being fun — I will retire 10 years later.”

Continuing his tale, Letterman said that he wanted to share an anecdote: Last fall, he went fishing with his 10-year-old son, Harry, and during the outing, they saw a giant, crazy-looking bird. So when Letterman got into work that following Monday, he spent the entire day making calls to bird societies, e-mailing the photo to his outdoorsy friends, and launching a full-scale investigation to find out what type of bird they saw. (Bald eagle? Golden eagle?) When he got home, his wife, Regina asked how his day was, and he started telling her all about the bird. Then Regina said, “That’s great — who was on the show?”

Much laughter from the audience as Letterman recalled his answer: “I said, ‘I don’t remember.'”

The moral of the story: That’s when he started seriously thinking about how long he wanted to keep doing the show. “If you spend most of your day trying to ID birds,” Letterman explained, “Should you really be running a network television program?”

That’s when Letterman got to point, saying he had just called up CBS chairman Leslie Moonves before Thursday’s show and said, “Leslie, it’s been great, you’ve been great, the network has been great, but I’m retiring.”

The audience, completely silent before breaking into nervous laughter, didn’t seem to know how to react as it became clear that Letterman wasn’t joking. “So we don’t have the timing of this precisely down, I think it will be at least a year or so,” he explained. “But sometime in the not too distant future – 2015 for the love of God, in fact, Paul and I will be wrapping things up and taking a hike.”

(Read a transcript of Letterman’s remarks here.)

Cut to commercial; when he came back, Letterman said, “I’m being told by the staff I just announced my retirement.”

Pretty much, as about the same time, news had leaked and the Internet started going crazy. During the taping, guest Johnny Depp appeared quite bewildered at how he wandered onto such a historic episode of the show, especially since it seems people were breaking down in tears backstage.

“There’s a lot of weepers, you have a lot of weepers back there,” Depp told Letterman after sitting down.

“What are you talking about?” Letterman asked.

“Apparently you just announced your retirement,” Depp said.

“Yes, I’m being told that happened moments ago,” Letterman laughed. “…I don’t remember anything about it.”

“There’s a lot of weepers back there. I myself was on the verge,” Depp said.

“No, please try to hold it together,” Letterman told him.

“It was only because I planned to announce my retirement,” Depp joked.

“Oh darn, what a night that would have been,” said Letterman, before quickly changing the subject.

And the matter was closed.