Area prevention manager Inspector Wil Black said the police approach was to "engage, encourage, educate and enforce".
"The students are our heart and soul and it will be great to have them back."
Otago University Students' Association president Jack Manning said OUSA was also excited to welcome students back.
"Just like during lockdown, we continue to be here to support and advocate for students, whether they are in Dunedin or elsewhere."
Hayne said in level 2, most learning would remain available online, so there would not be a "huge" change from Level 3 for using lecture theatres, apart from "limited teaching".
"We are still preparing for large-scale face-to-face learning at some stage in the future."
Contract tracing for staff and students would be recorded through the university's Wi-Fi and sign-in systems.
The six Dunedin campus libraries will reopen in stages, and with reduced hours, starting with the Robertson and Science Libraries and the ground floor of the Central Library on Monday.
"We aim to open the entire Central Library on May 20 and the Law and Health Sciences Libraries by Friday May 22."
Group study rooms and seminar rooms will be locked.
A library "click and collect" service would be available.
Campus cafes would open for takeaways only.
A university spokeswoman said students at halls of residence, who began to return on Thursday, would need to remain 1m apart and have staggered meal times.
She said social distancing was in place in colleges since the crisis began, as colleges had remained open looking after students.
Hayne said she was confident their "team of 20,000" would continue the fight against the virus.
"Those who stayed in colleges and diligently kept to their bubbles — it would not have been easy, but you have made us all proud."