Michael Sousa died nine days after the fall at Jane Austen College, in Norwich.
Opening an inquest into his death, coroner Yvonne Blake said the boy had "significant head injuries".
His life support machine was turned off at Addenbrooke's Hospital in Cambridge on 31 January. He died the next day.
The medical cause of death was given as severe traumatic brain injury.
A full inquest will be heard in August.
In a written statement, college principal Rebecca Handley Kirk said: "We are devastated by these events, and we send our thoughts and our love to Michael's family and friends.
"Michael had only joined us in September, but was already becoming a well-known student throughout the school, thanks to his lively personality."
A 12-year-old boy fell to his death from the top of a school stairwell just a day after his birthday, an inquest has heard.