Tercero "fled the United States via international air to Nicaragua prior to the discovery of Haley Anderson's deceased body," according to a statement released by police.
While the two were said to have only 'hooked up' and were never romantically linked, Tercero was said to have been obsessed with Anderson.
Anderson's roommates found her body lying in his bed after climbing in through a side window.
They say Tercero was angry because she had earlier dumped him for a different man.
"He never got over his obsession with her," Misha Topalli, Anderson's roommate and friend, told Time.
"They hooked up in the past, but to her, it was pretty platonic and she didn't want to have anything seriously," she added.
By the time police named him a suspect, Tercero was on board a flight back to Nicaragua where he has family.
He has since deleted his Facebook profile and Nicaraguan officials say they do not know if they will extradite him to face charges.
Police have not yet revealed how the young woman died or what condition she was found in but her friends said she appeared she had been dead for a while.
They also found a handprint bruise on her arm.
"She was in Orlando's room. She was in the bed. Looking back at it, she was clearly dead, because living people aren't that colour," Josephine Artin told the New York Post.
Artin said she had been laid there looking "very formal" but there was no blood in sight.
"There was no blood. The way she was lying, I wasn't sure if that's where she died or he put her there. It was very formal — she was on her back laying on the bed and she had a blanket halfway up her body. And she just had her arms at her side.
"There was a handprint bruise on her arm. When I saw that, that's when I knew for [sure] that Orlando had done this to her," she added.
Before fleeing to Nicaragua, Tercero allegedly told one of his sisters he had "done something bad" and "was a disgrace to their family", one of his roommates said.
In the weeks before her death, the students said Tercero drove past his alleged victim's home and once even slashed her tyres.
Anderson was last seen leaving her friends house after drinking wine and playing board games, last Friday.
The alarm was raised when she did not answer her phone the next day.
Anderson has been described as "bright" and "loving" by those who knew her.
Her co-worker, Athena Anadnostakos, who worked with her for years at Jazzman's Cafe on campus, spoke highly of the late student in a statement to Fox 40.
"She was a very good girl. She was friendly, joked around... we had a good time together," Anadnostakos told the news station.
"Everybody is sad... a lot of students came to New York together and they cried today. They were all so close," she said, in tears.
