The president's announcement reverses his longstanding opposition amid pressure from Democrats and even his own vice president. Mr. Obama became the first U.S. president to openly support gay marriage.
"I have hesitated on gay marriage in part because I thought that civil unions would be sufficient," Mr. Obama told Roberts. "I was sensitive to the fact that for a lot of people the word 'marriage' was something that invokes very powerful traditions, religious beliefs and so forth."
Mr. Obama described his thought process as an "evolution" that led him to this place, based on conversations with his own staff members, openly gay and lesbian service members, and conversations with his wife and daughters.
"I have to tell you that over the course of several years, as I have talked to friends and family and neighbors, when I think about members of my own staff who are in incredibly committed monogamous relationships, same-sex relationships, who are raising kids together, when I think about those soldiers or airmen or Marines or sailors who are out there fighting on my behalf and yet feel constrained, even now that 'Don't Ask Don't Tell' is gone, because they are not able to commit themselves in a marriage, at a certain point, I've just concluded that for me, personally, it is important for me to go ahead and affirm that I think same-sex couples should be able to get married," Mr. Obama told Roberts.
The president stressed that he still supports the concept of states deciding the issue on their own, and that this was a personal position.
North Carolina became the 30th state to adopt a ban on gay marriage on Tuesday. Six states - in the Northeast and Iowa - and the District of Columbia allow same sex marriages.
Mr. Obama's declaration injects a potentially polarizing issue going into the 2012 race for the White House. Polling suggests that the nation is evenly divided.
Republican presidential candidate Mitt Romney opposed same-sex marriage as governor of Massachusetts and says he has the same view now as then.
"States are able to make decisions with regard to benefits such as hospital visitation, benefits and so forth," he said. "My view is that marriage itself is a relationship between a man and a woman."
On Thursday, President Obama will be at a fundraiser at actor George Clooney's Los Angeles home. He is expected to land at Los Angeles International Airport around 6:30 p.m. The star-studded fundraiser is expected to raise $15 million.
The president raised a reported $1 million in the 90 minutes after his historic announcement on gay marriage.
Obama's stance elicits mixed reaction in Southland
President Obama's support of same-sex marriages is being hailed by gay rights supporters across Southern California.
West Hollywood has long carried the torch for gay rights. On Wednesday, West Hollywood City Councilman John Duran described the president's endorsement of same-sex marriage as a historic moment not just for his city, but for the country as a whole.
"This is a major step forward and it's truly a profile in courage," Duran said. "There's a great deal of political risk involved in taking this position, but I know in his heart he has always been with us, it's just great that he's now publicly with us."
After the president's announcement the Gay & Lesbian Alliance Against Defamation issued a statement, saying in part: "The arc of history today bent a little closer to equality for every American. As our nation draws closer to a more perfect union in which every person is created equal, we are left deeply encouraged by this truly watershed moment."
That's a feeling not everyone shares.
Randy Thomasson, the president of SaveCalifornia.com, a conservative group that has been battling the move toward legalized gay marriage, says the president's stance is politically motivated.
"Obama has showed he lied to the public four years ago when he said marriage is only for a man and a woman," Thomasson said. "So the president, although his duplicity is not surprising, he's actually going against the values of most voters and that is surprising that he's being that foolish."
Attorney Robert Tyler, who represents the Advocates for Faith and Freedom, says it's not up to the president to decide for the people of California.
"Every child has a mom, every child has a dad. They should have the right to know them and to be raised by them, it is the optimum situation for children," Tyler said. "It's ultimately going to be decided probably in our case, the Proposition 8 case, when it reaches the U.S. Supreme Court maybe later this year."
The Supreme Court would have the final say on gay marriage, but there's no telling when or if the high court will take the case.
ABC News and The Associated Press contributed to this report.