They, along with Chicago bluesman Buddy guy and ballerina Natalia Makarova, received this year's Kennedy Center Honors. The recognition is the nation's highest award for those who have influenced American culture through the arts.
The president jokingly described the honorees as "some extraordinary people who have no business being on the same stage together."
Mr. Obama thanked the members of Led Zeppelin for behaving themselves at the White House given their history of "hotel rooms trashed and mayhem all around," and he noted Letterman's humble beginnings as a weatherman in Indianapolis, where he once reported the city was being pelted by hail "the size of canned hams."
"It's one of the highlights of his career," the president joked.
All kidding aside, Mr. 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 said.
Meryl Streep first introduced the honorees Saturday as they received the award medallions 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.
The recipients were later saluted by fellow performers at the Kennedy Center Opera House in a show to be broadcast Dec. 26 on CBS.
The Associated Press contributed to this report.