Another man was taken to Royal Stoke Hospital with serious injuries which are not believed to be life threatening.
The crane also struck a neighbouring house.
Chief Superintendent Matt Welsted of Cheshire Police said: “This is a truly tragic incident, and our deepest condolences go out to the families affected at this extremely difficult time.
“This is a multi-agency operation and we are working closely with the Health and Safety Executive, Local Authority, and Building Control to establish the full circumstances of the incident, however I would like to reassure members of the public that nobody else is at risk.
“A residential property has been damaged as a result of the incident, the occupants were not injured and were checked over by medical professionals.
“They have since been relocated while the investigation continues.
“The bodies of those who have sadly lost their lives will shortly be recovered from the scene.
“I would ask that anybody who may have any footage of the scene, to please respect the families of those involved.
“Any footage that you believe could help officers with their enquiries, please send to our public contact email to allow us to effectively investigate the incident.”
Seddon is building a care home on the site where work started earlier this year.
Jonathan Seddon, Chief Executive, Seddon said: “There was an incident yesterday at our construction site on Dunwoody Way, in Crewe.
“I’m deeply saddened to say that following the incident involving the erection of a crane two people working on site have lost their lives, while a third remains injured in hospital.
“The crane also struck an adjacent house, the occupants were taken to hospital and have since been discharged.
“On behalf of everyone at Seddon I’d like to offer my heartfelt condolences to the family and loved ones of those who so tragically lost their lives yesterday.
“Our thoughts and prayers are with everybody involved, and words cannot express how we feel.
“At this time I cannot speculate as to the cause of this incident, but needless to say there will be a full investigation and Seddon is working closely with the emergency services and Health and Safety Executive.
“We will provide further updates once more information becomes available.”
“We will provide further updates once more information becomes available.”
Cheshire Fire and Rescue Service confirmed the bodies of the victims were recovered from the site shortly after midnight.
