"I'm more excited that he's here tonight than I'm able to explain," the ABC host, 44, said in introducing his CBS counterpart, whose career in late night stretches back to 1982.
Letterman, 65, who did two shows without an audience this week, returned the compliment, lauding Kimmel for being gracious despite their de facto rivalry.
"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," Letterman said. "Jimmy has broken that precept and has been nothing but generous and courteous and kind to me."
Letterman also thanked Kimmel for being in the city at such a difficult time. "God bless you for coming here," he said. "We're just now recognizing what has unfolded. To have you here, visiting New York City, is a nice thing."
Kimmel had some fun illustrating his decades-old Letterman obsession, showing photos of his Late Night-themed 18th birthday cake and "L8 Nite" license plate on his first car.
"Did your parents step in?" Letterman joked. "I mean, these are warning signs, Jimmy."
Kimmel took the opportunity to ask his guest a handful of personal questions, to which Letterman was generally forthcoming. Letterman characterized himself as a well-meaning but somewhat clueless dad to 9-year-old son Harry; as a hapless but happy fly fisherman; and as a largely anti-social person who really doesn't have any male friends at all.
"I don't know why that is," he said of the latter topic. "I don't think that at this point, and certainly not here on this show, that we're going to answer that question ... I think people don't like me."
They like him on television, to be sure. And soon, Kimmel will be his direct competition there, as he's moving to the 11:30 p.m. slot in January. Letterman graciously said he couldn't wait for that to happen.
"I want to wish you the best of luck when you move the show," he said. "I think it'll be exciting. I think you're going to be perfect at 11:30 ... I couldn't be happier than to have you in the running."