One of the victims was identified as 19-year-old Grace Kumar, a student at Nottingham University.
Another victim who was killed in the attack was identified as Barnaby Webber, another 19-year-old student at Nottingham University.
The third victim who was found dead in Magdala Road was named as Ian Coates, a school caretaker in his 60s.
Police were called to Ilkeston Road just after 4am on Tuesday where two people were found dead in the street.
Officers were then called to another incident in Milton Street where a van had attempted to run over three people.
A man, later identified as Ian Coates, has also been found dead in Magdala Road.
Chief Constable Kate Meynell said: “I can tell you that a 31-year-old man has been arrested on suspicion of murder and remains in police custody.
“We are not looking for anyone else in connection with the attacks and I can reassure the public that it is safe to visit the city centre – though there may be some road restrictions as we continue to establish what has happened.
“We are keeping an ‘open mind’ and are working alongside Counter Terrorism Policing to establish the facts – as we would normally do in these types of circumstances.
“My thoughts are with all the families affected by this horrific incident, and we are working extremely hard to understand exactly what has happened.”