David Webb, 43, from Cambridgeshire, was injured when the crane tilted and fell at a site in Crewe, Cheshire on 21 June. He died on 25 July as a result of his injuries.
David Newall, 36, from Bradford, and Rhys Barker, 18, from Castleford, West Yorkshire also died in the accident.
The Health and Safety Executive and Cheshire East Council are investigating.
More from Staffordshire and Cheshire
Mr Webb was originally from Northampton but was living in St Neots. His father died six days before he did.
His family said he died doing a job he loved and was passionate about.
"Dave was a fun loving character who lived his life to the full. He was known for his large personality and sung his way through life," a family statement said.
The building site, which was formerly part of the Bombardier works complex, belongs to Seddon Homes.
A nearby resident said he had seen the crane being used to lift tools when it started to tilt and then fall.
The HSE said it is aware of the incident and is working fully with Cheshire Police in its investigation.
A third man has died as a result of a crane collapsing at a building site.