Paul Crowther was initially charged with murder over the killing of Bethany Fields who died after suffering multiple stab wounds.
Miss Fields, 21, from Bramley, was found seriously injured on Fitzwilliam Street, Huddersfield, on September 21 last year.
Crowther, 35, of Elm Way, Birstall, pleaded guilty to manslaughter but not guilty to murder at a hearing at Leeds Crown Court on August 3.
That hearing was adjourned to allow time for the Crown Prosecution Service (CPS) to consider whether Crowther's plea was acceptable or if a murder trial should take place.
At a further hearing at the court today (August 20) prosecutor Jonathan Sharp confirmed that the manslaughter plea is acceptable.
It was expected that Crowther would be sentenced tomorrow (August 21) but the case was adjourned until next month.
Judge Tom Bayliss QC said he wanted a new sentencing date so he could hear evidence from three psychiatrists who have assessed Crowther.
The court heard today that it is agreed that Crowther has schizophrenia and an underlying personality disorder.
Crowther armed himself with a knife and 'lay in wait' for Miss Fields after finding out where she was before inflicting the fatal knife injuries.
Crowther will now be sentenced on September 8.
The defendant was not present in court for today's hearing but was represented by his barrister Stephen Wood QC.
Crowther is currently in custody at Newton Lodge secure hospital, in Wakefield.
At the hearing earlier this month, Mr Sharp said: "It is a highly emotional and sensitive case."
An inquest has heard the environmental geology student died after suffering numerous stab wounds.
A trial had originally been listed to take place in March this year but was adjourned so Crowther's mental health could be fully assessed.
After Miss Fields' death, relatives described how she had a bright future ahead of her.
In a statement released via the police, they said: "The life of Bethany, who was a beautiful, talented, ambitious, intelligent, kind, giving, and loving daughter, was tragically taken from her.
"A daughter, who any parent would have been proud of, much loved and respected by all; family, friends, work colleagues and fellow students.
"Bethany had a bright future ahead of her.
"She was studying environmental geography at university, travelling to Iceland to study the effects of glacial melts on the environment and to the Canary Islands to study volcanoes.
"She was musically gifted, starting on a music mentoring course and gradually during the holidays working at a studio.
"More recently, she worked with a charitable organisation for people with physical and learning difficulties. Through this, she brought much joy and pleasure into other people’s lives.
"Bethany had a wonderfully pleasant nature, with a love of nature, plants and animals.
"She will be sadly missed, but never forgotten, forever in our hearts and thoughts."