Police arrested Edwin Alcaide, 53, at his scheduled parole visit Thursday for the stabbing death of Lissette Torres, 19, on New Year's Eve of 1986, the New York Daily News reported.
Police re-opened the investigation into Torres' death 18 months ago and found a DNA match from fingernail evidence leading to Alcaide's arrest.
"When the new detective took over the case, I felt a sense of peace," Torres' mother, Rosa, said. "I had a renewed confidence that the case would be solved. ... Because an animal had committed such a horrific crime, I just knew that in time he would be caught."
Alcaide's criminal record includes convictions for assault, rape, robbery, attempted murder and drug charges, dating back to 1975.