Oliver Rutledge, 61, was operating a cherrypicker machine when the bricks collapsed on top of him.
The father of three died within half an hour of the accident on Fintona, Co Tyrone, in Northern Ireland.
Local priest Canon Patrick Marron said: "He went up to take down the chimney and it was rather windy, apparently the bricks just fell into the bucket.
"It was a terrible tragedy and shock for the people and there is a lot of empathy here."
Devoted father Mr Rutledge had only been at the site of the old Eccles Arms for a few days and was demolishing the last chimney on the sprawling three-storey premises.
A former grocery shop owner in Loughmacrory, Co Tyrone, he lived near Omagh in the county and was well-known.
Assembly member Barry McElduff said: "He was very well thought of by the people of Omagh. This is a reminder that the construction industry and the building trade, like farming, is one in which risks are faced every day."
The Health and Safety Executive and police are investigating.