Large crowds gathered at the Lincoln Memorial in the capital to hear America's first black president speak.
Referring to the turbulent 1960s, Mr Obama said: "There were couples in love who couldn't marry. Soldiers who fought for freedom abroad, but couldn't find any at home.
"America changed for you and for me."
But he pointed to the nation's economic disparities as evidence that Dr King's hopes remain unfulfilled.
The name of the original march was the March on Washington for Jobs and Freedom.
Mr Obama has said Dr King is one of two people he admires "more than anybody in American history", the other being Abraham Lincoln.
Thousands of people braved wet weather to attend the event.
Earlier, Oprah Winfrey said Martin Luther King Jr forced the US "to wake up, look at itself and eventually change".
The TV personality said the civil rights leader's lessons continue to inspire people all over the world.
Winfrey said Dr King recognised that all Americans shared the same dreams and that their hopes were not based on race.
She said King was right when he said all Americans' destinies are intertwined and would rise or fall based on how people treat their neighbours.
Winfrey said she asked her mother as a nine-year-old girl why her family was not there for the march. Winfrey said it took 50 years, but she finally arrived at the Lincoln Memorial to mark the anniversary of King's march.
Former US president Bill Clinton said the anniversary marks "one of the most important days in American history".
Mr Clinton said that march, and that speech, "changed America ... opened minds and melted hearts ... and moved millions".