Amanda Berry and Gina DeJesus identified themselves to police after running from a house in the 2200 block of Seymour Avenue near West 25th Street, WEWS-TV, Cleveland, reported.
"We've confirmed it's them," a detective told The (Cleveland) Plain Dealer. "They are alive and safe."
A third woman, Michelle Knight, also was found alive in the house, the TV station said.
"I heard screaming. ... And I see this girl going nuts trying to get outside," Charles, a neighbor who found the women, told the TV station. "I go on the porch and she said 'Help me get out. I've been here a long time.' I figure it was domestic violence dispute.
"She comes out with a little girl and says 'Call 911, my name is Amanda Berry.' ... When she told me, it didn't register." He said he placed the call and handed Berry the phone.
Hundreds of people were out in the street near the scene.
Berry, now 27, was last seen in 2003 as she left her job at Burger King, The Plain Dealer said. She disappeared the day before her 17th birthday, the newspaper said.
DeJesus, now 23, vanished in April 2004 at age 14 as she walked home from Wilbur Wright Middle School.
Both women's families had maintained they were still alive.
"I always said it from the beginning; she was sold to the highest bidder," DeJesus' mother, Nancy Ruiz, said in April 2012.
A witness told WEWS he helped break down the door of the house, where he saw a child about 4 or 5 years old with Berry, who he recognized from missing persons posters. He said he also saw other children inside the house.
Police told WKYC-TV, Cleveland, they had a 52-year-old man in custody and would be holding a news conference Tuesday morning.
The Plain Dealer identified the man as Ariel Castro, who has lived in the house since 1992. The TV station said records show he was arrested for domestic violence in 1993, but a grand jury declined to indict him.