Miguel Matias told investigators he strangled his daughter Ana with an electrical cord after he found her writing "sex things" on a computer in February 2008.
It was more than a year later, in April, when additional charges of sexual assault were filed after DNA tests uncovered he had impregnated her.
Matias, 35, initially pleaded not guilty and underwent a psychiatric evaluation after he tried to hang himself in prison. He was found fit to stand trial, but his attorney, Roy Schwartz, had asked for additional testing.
After the plea deal to second-degree murder, he faces the faces the maximum 25 years to life in prison, but could have gotten 50 years to life had the case gone to trial, Schwartz said.
"We had to do it. It's not a triable case," Schwartz said of the plea.
Ana and her two brothers lived in Allentown, Pa., with their mother, Jocelyn, after the couple separated, and they visited Matias occasionally. To neighbors and relatives, Matias was a doting father who bought the children presents and took them to restaurants.
But the man had a dark side, including a history of violence and mental problems that culminated in Ana's death.
Matias was institutionalized after trying to set a car on fire with his children inside in Pennsylvania, police said. Family members said it was only after one of his sons said goodbye to his sister that Matias changed his mind and decided not to torch the car.
It was not clear why he continued to have visitation rights. Family members said that before Ana's death, Matias had wanted to seek psychiatric help. They said he had applied for Medicaid insurance to cover the expense of counseling but was denied.
Matias called 911 the morning of Feb. 16, saying he had strangled Ana the night before and dumped her body in a wooded area of the Bronx, according to police.
But when officers searched his apartment building, for which he was superintendent, they discovered her body in the boiler.
During an earlier hearing, prosecutor Elizabeth McGrath read from a rambling statement Matias gave to police and prosecutors. It detailed how he initially picked up a bat _ but, fearing blood, instead tied a knot around an electrical cord and used it to strangle Ana.
"I want to serve 30 to 50 years," Matias said, according to the statement. "I strangled her. I choked her. I killed her."
Before he dialed 911, he phoned his cousin, Pablo Castillo, who rushed to the apartment, went down to the basement with police and saw a body in the boiler.
"I looked for about a second and then I could not look anymore. I saw part of a burned body. I couldn't look anymore. I couldn't believe it," he said in Spanish after the crime came to light.