Wu claimed that the messages she and her new husband received "were not only harassment but they were ageist, sexist and racist".
Hughes says that the emails have been "doctored". He is taking early retirement at the end of the month.
After receiving the emails in 2016, Wu complained to Bangor University's council and senior leadership team about Hughes' conduct. The university said that "action was taken by the university to resolve the issue" at the time.
Hughes, an expert in theoretical physics, took up the post of vice-chancellor at Bangor University in 2010 and the following year, his wife Wu was hired as Director of International Development.
At the time, the Association of Teachers and Lecturers called for an investigation into the appointment, saying it is "miraculous coincidence that these two people should find two highly paid jobs at the same institution at the same time … It seems extraordinary that a new post is being created at this time."
The university defended the appointment, saying the role had been advertised in 2009 but they were unable to find a suitable candidate.
Wu worked at the university until 2015, when she left to take up a post at Michigan State University.
Hughes was previously the President of Maynooth University in Ireland, where Wu also worked as the director of international development, according to her LinkedIn profile.
Earlier this month, several members of university staff were sent a tranche of personal emails he had apparently sent to his ex-wife and her new husband.
Hughes issued a statement to staff, saying that the emails had been "doctored" and apologising for any "distress or unease" caused.
He added: "The messages attached to this email dating from 2016 have been doctored and, whilst I do not want to go into details regarding what is clearly a very personal matter, I wanted to assure you that the messages are not what they seem."
Following his apology, the university confirmed that he would be relinquishing his role as vice-chancellor at the end of the month, rather than as originally planned at the end of the academic year in 2019.
A Bangor University spokesman said that university faced a number of challenges "many of which affect its strategy, direction and long-term success".
They went on: "It was agreed that it would be in the university's best interests for those issues to be dealt with by a team which will be able to see through the changes, not only during the forthcoming months, but crucially also into the next academic year.
"As a result, Professor Hughes agreed to step aside sooner than announced, and will be leaving at the end of December."
