Daniel Clifford Yeowell, 26, from Gillingham in Kent, who was working in a hole on a building site at Langley Green Primary School died on Monday afternoon after he was injured on site last Friday.
Sussex Police said the worker was hit on the head just after 11am and his condition was initially assessed as serious.
He was taken by air ambulance to the Royal London Hospital in East London.
A spokesperson for Sussex Police told the Crawley Observer: “Local police and the Health and Safety Executive are working together to investigate the circumstances.
“Nobody else was injured and no children were on the site which is sealed off from the rest of the school.”
Balfour Beatty is carrying out the school extension work.
The victim was working for a subcontractor.
A spokeswoman said: “Balfour Beatty is working with The Health and Safety Executive and Sussex Police therefore, it would be inappropriate to comment further at this time.
“The safety of its employees, subcontractors and the public is always Balfour Beatty’s main concern.”