The White House called Dylan "an icon of youthful rebellion and poetic sensitivity" and said Eastwood's films and performances are "essays in individuality, hard truths and the essence of what it means to be American".
"Obviously, their careers have marked the landscape of American culture for decades," Obama said, noting their absence from the ceremony in the East Room of the White House.
They were among 20 people and institutions recognised for their contributions to American culture through the arts and humanities.
Among those in the East Room to accept their awards were author, activist and Holocaust survivor Elie Wiesel for his work to educate the country and the world on the Holocaust, and conductor Michael Tilson Thomas for his efforts to expand audiences and the repertoire for contemporary music.
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Soprano Jessye Norman was recognised for "broadening contemporary operatic repertoire".
Maya Lin earned a medal for her architecture, including the National Vietnam Veterans Memorial, one of Washington's most visited monuments.
Obama also awarded composer John Williams a medal for music featured in films such as the Star Wars series and the soundtrack to the Olympics.
Noting that the United States has produced talents ranging from Mark Twain to Toni Morrison, John Philip Sousa to Louis Armstrong,
Obama praised the US diversity.
"They bring us joy, they bring us understanding and insight, they bring us comfort in the good times and perhaps especially in difficult times in our own lives and the life of our nation," he said.
