David Letterman sent this witty rejection letter to Jimmy Kimmel in 2002

On Wednesday, David Letterman will host the "Late Show" for the very last time.

Out of respect for his idol, Jimmy Kimmel will air a re-run of his competing late-night show.

"I have too much respect for Dave to do anything that would distract viewers from watching his final show," Kimmel recently told The New York Times. "Plus, I'll probably be crying all day, which makes it hard to work."

Indeed, Kimmel did shed a few tears during his tribute to the veteran late-night host on Tuesday. But Kimmel's obsession with Letterman goes way back.

Kimmel, 47, has idolized David Letterman, 68, since the younger late-night host was a quirky kid growing up in Vegas.

"His show was just so weird and different," Kimmel told Rolling Stone back in 2013. "I'd never seen anything like it. I didn't know anyone who had a sense of humor like that."

Kimmel has often joked that the only reason he went into show business was to be friends with Letterman - and wondered why anyone would watch his show instead of Letterman's.

So, when Kimmel was coming off four years as co-host of Comedy Central's "The Man Show" and about to debut "Jimmy Kimmel Live!" on ABC in 2002, naturally he reached out to Letterman to be a guest on the show's premiere episode.

Letterman's typed response - on personal stationery - today sits framed on Kimmel's desk in his studio office, alongside a photo of his late grandparents and a picture of himself covered in whipped cream after popping a fictional zit on Jon Stewart's forehead.

This is what the letter said. It's from Sept. 23, 2002, and was uncovered by New York Magazine.

Dear Jimmy,

Thanks for asking me to appear on your premiere. Unfortunately, I will be out of the country on business. I'm sure the program will be a success regardless.

Sincerely,

Dave

"His response is hilarious," Kimmel told New York Magazine. "He's not out of the country on business. He knows you know he's not out of the country on business and just the words 'on business' - it really makes it a perfect letter for me."

Eleven years later, the two aren't exactly best buddies, but Letterman did appear on "Jimmy Kimmel Live!" for the first time in 2012 as the L.A.-based show broadcast out of Brooklyn after Hurricane Sandy.

Letterman's appearance gave Kimmel his biggest Wednesday audience in the show's history - about 2.4 million viewers.

Leading up to the visit, Kimmel said he was "terrified" to interview Letterman and tried to justify it by saying, "I'm sure for him it's nothing more than a nuisance, that he's just doing it to be nice."

But Letterman was a gracious guest as Kimmel showed him photos of his "Late Night"-themed 18th birthday cake:

And "L8 Nite" license plate on his first car.

Letterman responded by telling his No. 1 fan, "I'll be honest with you, it was troubling. I kept saying to people, 'Why is he sucking up to me?' ... When I was persuaded that there was some measure of stability here, then I really realized that it was genuine and I couldn't appreciate it more."

Letterman added, "In show business, one of the precepts is you're not really supposed to be nice to people, especially if you have the same occupation as another person. Jimmy has broken that precept and has been nothing but generous and courteous and kind to me."

As a kid, Kimmel told Rolling Stone that he felt like Letterman was doing his show "specifically for [him]." And now, to return the favor, Kimmel won't do his show on Wednesday, specifically for Letterman.

Watch Letterman's ratings-raising 2012 appearance on "Jimmy Kimmel Live!"

On Tuesday, Kimmel gave an emotional farewell tribute to Letterman, urging viewer's to watch Dave's final show on Wednesday instead of his own.

Through tears, Kimmel explained: "Dave is the best and you should see him."