Ohio Attorney General Mike DeWine said preliminary tests confirmed Castro's paternity, The Cleveland Plain Dealer reported.
DeWine said state lab technicians had worked through the night to produce the results.
Castro's DNA also was compared to samples from other crime scenes around the state, but no matches were found,
Castro is accused of kidnapping, raping and beating three women and holding them captive for a decade.
One of his Castro's adult daughters, Angie Gregg, says her father "is dead to me."
"There will be no visits; there will be no phone calls," she told CNN in an interview Thursday. "He can never be 'daddy' again. I have no sympathy for the man."
"I wonder this whole time, how he could be so good to us, but he took young women, little girls, someone else's babies, away from these families and over the years never felt enough guilt to just give up and let them free," Gregg said.
Castro, a 52-year-old former bus driver, allegedly enticed the women off the street with offers of a ride home, authorities said.
He was held in jail Friday on $8 million bail under a suicide watch after being charged with rape and kidnapping for allegedly abducting Berry, Gina DeJesus and Michelle Knight. Authorities say Castro repeatedly raped the three women during their years-long ordeal.
He has also been accused of beating at least one of the women until she had a miscarriage. Cuyahoga County Prosecutor Timothy McGinty said the miscarriages could be grounds for the death penalty.
During a brief arraignment Thursday, Castro was also charged with kidnapping the daughter Berry gave birth to in captivity, who is now 6.
Castro didn't enter a formal plea during the court hearing. Public defender Kathleen DeMetz had no comment about whether Castro was guilty.
An official with knowledge of the investigation told The New York Times the women's captivity was "depraved beyond your imagination."
McGinty said Ohio law allowed for the death penalty for the "most depraved criminals who commit aggravated murder during the course of a kidnapping."
A police report obtained by the Times and CNN said Knight told police she had been impregnated several times during the ordeal but miscarried each time after Castro starved her for two weeks or more and then repeatedly punched her in the abdomen.
McGinty said he was considering whether to ask a grand jury to consider capital murder charges against Castro. The grand jury is expected to hear evidence in the coming days and could indict Castro on additional charges, The Washington Post said.
The women and the girl were rescued Monday night after Berry, 27, hailed a neighbor while Castro was out, kicked in part of the front door with the neighbor's help and frantically called 911.
The women told police Castro had first kept them chained in the basement but eventually let them live on the second floor.
An official told the Times the women described how they "were brought into the room and out of the room, when the chains were on, when the chains were off," as well as when they were rewarded with trips to the toilet and occasional showers.
Cleveland Mayor Frank Jackson ordered police to stop divulging information about the case "outside of the established chain of command."
Dennis Rodman pledges to end trips to North Korea
Scarlett Johansson steps out with fiance after pregnancy reveal