The Australian Human Rights Commission report also found that almost 7% of students were sexually assaulted on at least one occasion in 2015 or 2016.
Women at university were more likely than men to be assaulted or harassed, the commission found.
The milestone study is said to be the largest of its kind in Australia.
Sex Discrimination Commissioner Kate Jenkins said the report painted a "disturbing" picture of university life.
"It is confronting to learn that sexual assault and sexual harassment are a common part of these students' experiences in their academic, their social and their residential life," she said.
"Sadly, the impacts of these experiences have devastating impacts and it can be life-changing, affecting health, studies and future careers."
The study of 39 universities and 31,000 students found that sexual assault and harassment had occurred in varying degrees in all university settings.
It defined sexual assault as being "when a person is forced, coerced or tricked into sexual acts against their will or without consent, including when they have withdrawn their consent".
Unwanted conduct of a sexual nature, such as inappropriate leering or comments, constituted sexual harassment.
"One in five of those who were sexually assaulted said that this occurred at a university or residence social event," said Ms Jenkins.
"We found that college settings are a particular area of concern, particularly for women who were four times as likely as men to have been sexually assaulted in this setting."
The survey also found:
- 51% of sexual assault victims and 45% of harassment victims knew some or all of the perpetrators
- bisexual and asexual students were the most likely to be sexually assaulted
- the majority of perpetrators were male
A university setting was defined as on campus, at an event organised or endorsed by the institution, or on technology - such as the internet - where perpetrators were university-related.
University of Queensland Vice-Chancellor, Peter Hoj, said the statistics were very concerning.
"The report indicates that about 1.6% of students are sexually assaulted in a university setting nationally - there is only one acceptable number and that is zero," he said.
"There is no place for those unacceptable behaviours at university or in the wider society."
The report authors called on universities to improve their responses to assaults and harassment.