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Valdo Calocane, 32, denied murdering Barnaby Webber, Grace O'Malley-Kumar and Ian Coates on 13 June this year, but pleaded guilty to their manslaughter on the grounds of diminished responsibility.
He also pleaded guilty to attempting to murder three others.
Prosecutor Karim Khalil said the Crown Prosecution Service (CPS) would need further time to decide whether to accept Calocane's pleas.
University of Nottingham students Ms O'Malley-Kumar and Mr Webber, both 19, had been celebrating the end of their exams when they were stabbed to death as they walked home from a night out.
School caretaker Mr Coates, 65, was also killed on his way to work at Huntingdon Academy.
Calocane, who was himself a former student at the university, also hit three pedestrians - Wayne Birkett, Marcin Gawronski and Sharon Miller - while driving Mr Coates' van in Milton Street and Upper Parliament Street, in the city centre.
He was arrested on the day of the attacks.
Calocane, who answered to the name Adam Mendes, appeared in the dock at Nottingham Crown Court dressed in a dark suit and looked straight ahead during the 15-minute hearing.
Judge Mr Justice Turner adjourned the case until 16 January next year.
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Thousands of people attended vigils for the victims at the university and in the city centre in the wake of the attacks.
Medicine student Ms O'Malley-Kumar, a hockey player from Woodford, in east London, was described by her family as being "loved endlessly by all" and "resilient and wise beyond her years".
The family of Mr Webber, a keen cricketer who was studying history, said he was "an extraordinary 'ordinary' person".
Speaking at a memorial cricket match for her son and his friend in September, Emma Webber said she misses his "beaming smile".
Two of Mr Coates' sons said his death had "rocked everyone's world", adding: "Nobody deserves this but he definitely didn't."