On Saturday, police arrested Chanel Lewis, 20, outside his home in Brooklyn.
Boyce says the encounter that led to 30-year-old Vetrano's death apparently was a chance one. I just lost it.
"This is a very good day for justice in New York City", Boyce said.
She posted later that she was at a "loss for words". Her father normally ran with her but was injured that day.
Karina was reported missing by her father, a retired firefighter who usually joined her during her jog, but decided not to on August 2. She had touch DNA on her back and there was more DNA on her cellphone.
The dad said he would tell Vetrano's family, "I'm sorry to hear about [your daughter], but I'm sure that [Chanel] would not be a part of that".
'And about 25 minutes later I got a bad feeling. "I want to see his face".
"My daughter, barely 100 pounds, fought her last moments alive, fighting this evil savage".
She left her home for a jog at around 5 p.m. on August 2. "The police did an excellent job", dad Phil Vetrano said.
The man was interviewed on Tuesday, and he volunteered a DNA sample and the results came back Saturday, sources say.
It has led to the arrests and convictions of other unsafe criminals but is not common practice in NY.
Police had issued chilling CCTV footage of her last moments.
Police also said that Lewis made "detailed, incriminating statements and admission" during questioning. He lives in East New York with his mother, and police said they do not believe he was stalking or knew Vetrano.
Lewis does not have a prior record. "But it was nothing he's ever acted on".
Lewis, police said, was identified through a number of factors, including DNA evidence taken from Vetrano's person, a 911 call, and several court summonses that linked him to the area.
Assistant District Attorney Michael Curtis said: "This defendant admitted to attacking the victim, admitted to beating her, to strangling her and dragging her body into the weeds".
But Lewis' father, Richard Lewis, paints a much different picture of his son.
Authorities said Lewis did not know Vetrano before the attack.