Michael Kydd, a part-time business instructor at Mount Saint Vincent University, held a news conference to announce his resignation and apologize to his wife, children and the school.
"I'm not here to point fingers at anybody," he said, his voice sometimes cracking with emotion. "I'm here to point the finger at myself. I made a serious error in judgment. ... I expect my career to be ruined."
Kydd said he met the 38-year-old student through a distance education course he was teaching in October 2014 while he was separated and seeking a divorce.
The relationship with the student involved two sexual encounters and was consensual, he said.
However, he admitted his actions violated the university's code of conduct, noting that the university had launched a disciplinary investigation.
Ramona Lumpkin, the university's president, said the school decided to notify students as soon as it was aware the situation was being made public.
"We're taking the whole incident very seriously," she said.
Lumpkin said she was first approached Dec. 23 about the allegation but the student wanted to consider over the holiday break whether to take action. The university reopened Jan. 2 and the student filed a complaint Wednesday, she said.
Asked why he decided to use such a public venue to resign, Kydd said: "I did not want to compound my mistake ... by failing to come forward and take responsibility for what I have done."
The woman told CTV she and Kydd had a mutual sexual relationship and she confirmed explicit images were exchanged.
"Initially, I had said that I did not want anything that happened between him and I, as two people, to get mixed up in the classroom," said the woman, who was not identified.
CTV reported the woman became uncomfortable with the relationship when she told Kydd she couldn't write an exam because of a personal emergency and he told her not to worry about it.
"I questioned him, this was through text ... and he said don't worry about writing it," she said.
She said she went to the university because she felt her relationship with Kydd affected the school's integrity.
During his news conference, Kydd said he decided not to include the failing mark from the woman's exam in her final grade.
"That's a mistake that I made," he said.
The university announced its investigation after an explicit image of Kydd was posted on Twitter on Thursday morning by Glen Canning, the father of Rehtaeh Parsons.
Canning said he had received copies of sexual messages allegedly sent from a Mount Saint Vincent professor to a student.
Canning has campaigned against cyberbullying since his daughter died at 17 after a suicide attempt that followed months of online harassment.
— With files from Sue Bailey in St. John's, N.L.