The college denied the charges, but was convicted last week of failing to ensure children’s safety between August and September 2012.
Nursery nurse Sophee Redhead was cleared of manslaughter by gross negligence.
The trial at Leeds Crown Court heard how three-year-old Lydia died after becoming entangled on a rope attached to a slide in the nursery’s outdoor area.
The court was shown CCTV evidence of a rope left overnight on the slide in the hours before Lydia’s death and heard it had been left out on previous occasions.
The risk of children injuring themselves by getting the rope tangled round their necks was identified in a college risk assessment, which said all ropes should be put away after use. The assessment also stated that the rope and slide should only be used under supervision.
In a statement, Alison Birkinshaw, principal and chief executive of York College, said, ‘We remain deeply saddened by the events of 17 September 2012 and we know that no family can ever recover from the death of a child. Nothing can reduce the pain felt by Lydia’s family and we are truly sorry for what has happened. Lydia and her family will be forever in our thoughts.
‘We remain committed to learning from these tragic events and took the difficult decision to close the nursery permanently immediately after the tragedy.’
She added that the college had since brought in the British Safety Council to conduct a full inspection of health and safety across the college sites.
In another case where a child died at nursery, Casterbridge Care and Education Limited and Casterbridge Nurseries (Eton Manor) pleaded guilty to health and safety failings.
Rhiya Malin died after becoming trapped in a playhouse at Eton Manor Children’s Day Nursery in Chigwell, Essex, in 2007.
Both nursery companies were fined £75,000 each and ordered to pay £70,000 in costs to Epping Forest District Council, which brought the prosecution case.
Bright Horizons acquired Casterbridge Nurseries in May 2012.