Forty-two year-old James Kiloh, from Aberdeen, and Anthony Doherty, 45, from Derby, died after spending around 40 minutes in the water.
Mr Kiloh fell overboard on Thursday afternoon during a routine inspection of the unmanned MCP-01 platform, which is operated by Total and lies around 100 miles North-east of Peterhead.
He then became trapped between the inner core of the platform and the outer breakwater wall as colleagues tried to reach him.
Mr Doherty, who was on board a fast rescue craft, jumped into the water and climbed through a hole in the outer wall in an attempt to reach Mr Kiloh.
He managed to grab Mr Kiloh but lost his grip, and it is thought he may then have detached the lifeline he had fastened to himself.
Both men were recovered from the water after about 40 minutes and flown to hospital in Aberdeen, where they were later pronounced dead.
Mr Doherty worked for Vector Offshore. Mr Kiloh, who was married with an eight-year-old son, Lee, worked for McGregor Energy, and was part of an 18-strong maintenance team sent to the platform.
He is thought to have slipped from the walkway during a routine inspection, and fell around 40ft to the water below.
Both men were eventually recovered from the water when helicopter co- pilot Neil Gordon managed to reach them with the help of a portable ladder.
A top-level inquiry into the tragedy was launched, with Health and Safety Executive officers, police and members of Total's own inspection team due to fly out as soon as weather conditions permitted. Lucien Lallier, managing director of Total Oil Marine, said the company was "shocked and saddened" by the deaths, the first to occur at one of its platforms in recent years.
He added that all the companies involved wanted to express their deep sympathy to the bereaved families.
It is thought that conditions inside the concrete breakwater would have been even colder than in the open sea, and that both men suffered hypothermia.