While walking through Spring Creek Park, Lewis came across Vetrano, 30, who was out jogging alone.
"She was running toward me and I just lost it," Lewis told investigators during questioning, according to the prosecutor. "She didn't do anything. I was just mad at that time. I beat her to let my emotions out. I never really meant to hurt her, it just happened."
In another statement, Lewis said of Vetrano: "I fought with her for five minutes. She scratched my face. I hit her about five times and I knocked her out. Her teeth broke. I got madder and madder and I strangled her."
Lewis also said that Vetrano's shorts came off while he was dragging her into some bushes after she fell into a puddle. He has previously denied allegations of rape.
The victim's mother, Catherine Vetrano, showed no visible emotion in court. She was accompanied by husband Phil, who was the one who found their daughter's battered body in a secluded marsh after she failed to return home from a jog.
Lewis was arrested in early February, nearly six months into the search for Vetrano's killer, after he gave a voluntary cheek swab which matched DNA found under the victim's fingernails.
While in custody, Lewis said he was sorry for his actions and asked to be given an opportunity to apologise to Vetrano's family.
At one point he told a detective: "tell my mom that I'm sorry."
Following Tuesday's arraignment, Lewis was remanded back to jail to await his next court appearance scheduled for July 13.
The Legal Aid Society, which is representing Lewis, issued a statement saying it 'looks forward to closely reviewing' prosecution documents.
It has previously said it was concerned about how DNA was collected and about 'the overall reliability' of evidence in the case.
Lewis' mother, Veta, has said he has mental health problems but would not hurt anybody.
Speaking to reporters outside Queens County Supreme Court on Tuesday, the mother proclaimed Chanel's innocence and accused law enforcement officials of framing her son.
"I know that there is a God, and I know that justice is coming for my child," Veta Lewis stated.