Bowmer and Kirkland, Advanced Roofing and JKW Roofing Services were working on a new three-storey teaching block at Abbotsfield School for Boys in Hillingdon, west London, when the accident happened on 23 February 2017.
Westminster Magistrates' Court was told that, because of 94 mph winds, there were several warnings on site and many activities had been suspended.
However, the roof works continued until early that afternoon, when the director of JKW Roofing, John Whitham, was blown off the roof along with freestanding A-frame barriers and stacks of insulation.
The 52-year-old sustained severe injuries to his pelvis, back and leg.
Bowmer and Kirkland was the principal contractor. The roofing works were contracted to Advanced Roofing, which subcontracted some of the works on the main building to JKW Roofing.
An investigation carried out by the Health and Safety Executive (HSE) found all three companies had failed to properly assess the risk of high winds during work at height.
It said they had taken an "informal approach to assessing weather conditions which was not in line with industry standards".
Bowmer and Kirkland pleaded guilty to breaching reg 4(3) of the Work at Height Regulations. It was fined £350,000 and ordered to pay £6,190 in costs.
Advanced Roofing was handed a £29,300 fine plus £6,188 costs after it admitted breaching reg 4(3) of the same regulations.
JKW Roofing, which pleaded guilty to the same breach, was handed a 12-month conditional discharge and ordered to pay £6,160 in costs.
HSE inspector Gabriella Dimitrov said: "If a suitable safe system of work had been in place prior to the incident, the life-changing injuries sustained by Mr Whitham could have been prevented."