David Connelly, 40, was taken to hospital following the industrial accident in Tomago, New South Wales.
He was in a medically induced coma but his family agreed to switch off his life support machine last Friday after doctors revealed there was no hope of recovery.
His father Jim Connelly, who moved his family from Glasgow to Australia and worked at the same firm before retiring three years ago, said: "We agreed to him being an organ donor – it's what David would have wanted.
"We've just learned his organs have helped three people."
David had worked at steel supplier Martensite Australia for seven years.
An investigation into the accident is under way and funeral plans are on hold until his body is released.