The president hailed Holbrooke as one who led an "extraordinary life" and "served his country until his final moments."
"He recognized that our prosperity is tied to that of others; that our security is endangered by instability abroad, most importantly, that our moral leadership is at stake when innocent men, women and children are slaughtered through senseless violence -- whether it's in Srebrenica or Islamabad," the president said.
"It was clear that Richard was not comfortable on the sidelines. He belonged in the arena."
The president announced the creation of an award named after Holbrooke that will award excellence in American diplomacy.
Remembering him as a "hurricane of eloquence and energy and force," former president Bill Clinton praised the late statesman's career and his perseverance.
"He was a good diplomat because he was smart and he could learn and he could think. He could write. He could speak, and most important, because he could do," Clinton said. "And he loved the doers."
Holbrooke's family remembered him as a man who dedicated his life to public service.
"Elegance was about the spirit of the mind. He was an elegant man," said his wife, best-selling author and journalist Kati Marton. "From Richard, I learned a life of meaning is better than a life of ease, and perhaps even better than a long life."
Holbrooke joined the foreign service in 1962. Like many diplomats of his generation, he began his career against the backdrop of the war in Vietnam.
The late diplomat's career took him around the world -- from Morocco, where he served as director of the Peace Corps there in the early 1970s, to Asia, where he worked in Jimmy Carter's administration.
But Holbrooke is best remembered for brokering peace talks in the Balkans in the mid-1990s as assistant secretary of state for Europe. He drafted the Dayton Peace Accords that ended years of brutal fighting in Bosnia.
"Richard possessed a hard-headed, clear-eyed realism about how the world works. He was not naive but he also believed that America has a unique responsibility in the course of human events. He understood American power, and all its complexity, and believed that when it is applied with purpose and principle, it can tip the scales of history," the president said today.
"That coupling of realism and idealism -- which has always represented what is the best in American foreign policy -- that was at the heart of his work in Bosnia where he negotiated and cajoled and threatened all at once, until peace was the only outcome possible," he said.
At the time of his death, Holbrooke was Obama's special envoy to Pakistan and Afghanistan.
The memorial today was held at the Kennedy Center because it was President John F. Kennedy who created the Peace Corps, in which Holbrooke served, and inspired him to a career of public service, said David Rubenstein, co-founder and managing director of The Carlyle Group, an investment firm where Holbrooke spent some of his later years.