The two performers were among the five recipients of this year's Kennedy Center Honors, which annually award individuals for their contribution to US culture.
The other honorees at the ceremony were veteran comedian Mel Brooks, jazz pianist Dave Brubeck and opera singer Grace Bumbry.
The event, held in The White House's East Room, was followed by a gala concert in Washington, DC's Kennedy Center, in which President Obama and his wife Michelle joined a host of big-name stars paying tribute to this year's honorees.
Bruce Springsteen's friend Sting got the President and the First Lady on their feet with a rousing performance of Bruce’s song The Rising.
Meanwhile actress Meryl Streep praised colleague Robert De Niro’s friendship and talent.
"(He) saw humanity in (characters) who at first glance seemed inhuman," she said.
Other stars present on the night included Jack Black, Ben Stiller, Sharon Stone, Martin Scorsese, Matthew Broderick and Aretha Franklin.
"We worked really hard for our music to be part of American life and our fans' lives," said rock singer Bruce on being awarded the honour.
"So it's an acknowledgement that you've kind of threaded your way into the culture in a certain way. It's satisfying."
The gala capped off a busy weekend for the five award recipients, which also included a dinner hosted by US Secretary of State Hillary Clinton on Saturday night.