Lewis is charged with second-degree murder after the medical examiner's lab matched DNA evidence from the crime scene and Vetrano to the suspect, police said.
Lewis is being held without bail. A grand jury could issue a formal indictment soon.
Meanwhile, Vetrano's family is taking steps to honor her memory. They went to Cuba last month, where Vetrano had planned to run a November marathon. They sprinkled some of her ashes in a quiet park.
Her father, Philip Vetrano, said he has disbursed nearly $300,000 in GoFundMe donations made in Karina's honor. So far, the donations have included a check to Archbishop Molloy High School for a scholarship in Karina's honor, according to the GoFundMe page.
UPDATED STORY: What we know about Chanel Lewis, Karina Vetrano's suspected killer
DNA was obtained from Lewis through a voluntarily cheek swab. It was taken previously from under Vetrano's fingernails, behind her ear and on her cell.
Lewis, who does not work, has no prior arrests. He lives in East New York with his mother, and police said they do not believe he was stalking or knew Vetrano.
Vetrano, 30, left her home for a jog around 5 p.m. on Aug. 2. When she failed to return, family members reported her missing and started searching for her.
Her body was found around 9 p.m. by her father about 14 blocks from her home, in the marshes of Spring Creek Park, off 161st Avenue and 78th Street. She was about 15 feet off the trail.
The medical examiner's office performed an autopsy and ruled Vetrano's death a homicide, saying she was strangled.
The next court date was set for April 17. null