Ahead of the ceremony, Obama hosted a reception in the White House East Room for this year's award recipients: actor Al Pacino, The Eagles rockers, singer James Taylor, gospel singer and civil rights activist Mavis Staples and Argentine pianist Martha Argerich.
"The Kennedy Center Honors are about folks who spent their lives calling on us to think a little to harder and feel a little deeper and express ourselves bravely and maybe take it easy every once in a while," Obama said, calling the gala "one of the parts of the job that I will miss."
Obama jokingly asked Eagles guitarist Joe Walsh, a notorious troublemaker, to not trash the White House because he is leaving soon and wants his "security deposit" back.
The Eagles were set to be honored last year but postponed due to the illness of founding member Glenn Frey, who died in January. He received the Kennedy award posthumously.
At a reception hosted by Secretary of State John Kerry on Saturday, Kennedy Center chairman David Rubinstein handed the artists medallions and hung wide rainbow-colored ribbons around their necks.
"In 1968, when James Taylor signed with Apple Records, I was in Vietnam and America was at war abroad and in turmoil here at home. We were fighting and marching to the music of (Jimi) Hendrix, the drumming of Ringo (Starr), the Doors, the (Rolling) Stones, and the (Grateful) Dead," Kerry said.
"And amid the darkness of that era, James Taylor returned sunlight to our minds, conjuring up the warm images of snow on the turnpike from Stockbridge to Boston, deep greens and blues as the colors of choosing, and moonlight ladies singing rockabye to 'Sweet Baby James.'"
Taylor, 68, performed "America the Beautiful" at Obama's second inauguration in January 2013, while 77-year-old Staples, who represents the music score of the civil rights movement, sang at John F. Kennedy's inauguration.
Pacino's breakthrough role was as Michael Corleone in "The Godfather" (1972). Now 76, he has performed in some 100 films and plays over the course of a lengthy career, including in "Scarface, "Sea of Love," "Heat" and "Scent of a Woman."
Argerich, 75, is widely considered to be one of the world's best, if very reclusive, living pianists. For nearly two decades, she largely shunned solo performances, playing almost exclusively with orchestras and chamber ensembles, until a sold-out recital at Carnegie Hall in New York in 2000.
In a recent interview, Argerich told The Washington Post she was "perplexed" about why she had received the award.
"I don't understand, because I think I haven't done much in America,? she added.
But Argerich has clearly made her mark, having performed with the New York Philharmonic Orchestra, the Boston Symphony and other top American orchestras.
The star-studded yearly gala is a high point on Washington's society calendar.
On December 27, CBS television will broadcast the event, a fundraiser for the national arts center that is a living memorial to Kennedy.
The awards recognize performers' lifetime contributions to American culture through the arts.
Kerry said honoring the performers served as a reminder for the nation that "even amid the turbulence, even amid the tragedies, there is something truly magical about the human spirit -- its ability to bounce back and feel joy, its capacity to move in beguiling ways, and its utter refusal to give in to darkness -- the light is always there."