Obama elicited laughs from his guests when he described the honorees as "some extraordinary people who have no business being on the same stage together."
Noting that Guy made his first guitar strings using the wire from a window screen, he quipped, "That worked until his parents started wondering how all the mosquitoes were getting in."
The president thanked the members of Led Zeppelin for behaving themselves at the White House given their history of "hotel rooms trashed and mayhem all around."
"It's fitting that we're doing this in a room with windows that are about three inches thick and Secret Service all around," he said to laughter from the diverse group of artists.
Obama went on to note Letterman's humble beginnings as an Indianapolis weatherman, who once reported the city was being pelted by hail 'the size of canned hams.'"
"It's one of the highlights of his career," he said.
All kidding aside, Obama described all of the honorees as artists who "inspired us to see things in a new way, to hear things differently, to discover something within us or to appreciate how much beauty there is in the world."
"It's that unique power that makes the arts so important," he added.
Later on the red carpet, Letterman said he was thrilled by the recognition.
"It supersedes everything, honestly," he said. "I haven't won that many awards."
Meryl Streep first introduced the honorees Saturday during a formal dinner at the U.S. State Department hosted by Secretary of State Hillary Rodham Clinton and attended by celebrities including comedians Stephen Colbert and Jimmy Kimmel, and Letterman's longtime band leader, Paul Shaffer.
Clinton noted the ballerina Makarova "risked everything to have the freedom to dance the way she wanted to dance" when she defected from the Soviet Union in 1970.
Makarova quickly made her debut with the American Ballet Theatre and later was the first exiled artist to return to the Soviet Union before its fall to dance with the Kirov Ballet.
Clinton also took special note of Letterman, saying he must be wondering what he's doing in a crowd of talented artists and musicians.
"Dave and I have a history," she said. "I have been a guest on his show several times, and if you include references to my pant suits, I'm on at least once a week."
The crowd gave Clinton a standing ovation as she hosted her final salute to the nation's artists as secretary of state.
Kennedy Center Chairman David Rubenstein gave her a subtle nudge to run for president in 2016, saying there's another room at the State Department to name after a secretary who later becomes president.