Renatas Timofejevas, 36, was fatally injured in the incident at the Alba Proteins plant near Dumfries at about 1540 GMT on Tuesday.
Both Dumfries and Galloway Constabulary and the Health and Safety Executive (HSE) are investigating the accident.
A police spokesman said Mr Timofejevas' family in Lithuania had been informed of his death.
Alba Proteins is part of the Leo Group which specialises in the processing of animal by-products.
The company has said it will co-operate fully with both investigations.