The men were taking out a mezzanine floor in a warehouse that had been bought by George Simms, a partner in Simco Services, who brought in the two men to dismantle it.
The incident was investigated by the Health & Safety Executive (HSE), which prosecuted George Simms for a breach of the Work at Height Regulations.
HSE told Leeds Magistrates court that Mr Simms had not considered how the work should be undertaken and there were no safeguards to prevent them falling. The men were repeatedly required to work close to the open edges, often while carrying materials and tools, making a fall more likely.
The investigation was unable to identify exactly how the two workers fell together but it is thought that a board broke, causing the men to fall to the concrete floor below.
George Simms, of Ramshead Drive, Seacroft, Leeds, was fined £2,000 and ordered to pay £3,210 in costs after admitting a breach of Regulation 4(1) of the Work at Height Regulations 2005.
After the hearing, HSE inspector Martin Hutton said: "The two men who fell from height could easily have been killed. While one has been lucky enough to make a good recovery, the other suffered lasting spinal injuries which meant he had to give up work.
"As far as Mr Simms goes, his only method of work was an unsafe, poorly-planned one, presenting abundant risks to workers of falling off or through the mezzanine.
"Work at height is the single biggest cause of fatal incidents in the workplace and proper planning is vital to ensure it can be carried out safely. That includes choosing the most suitable equipment and making sure work is properly supervised."