The body of Ross Flett was discovered on the Transocean Rather drilling platform by his colleagues on Sunday.
The 35-year-old was a ballast control operator and had worked for the oil and gas firm for more than six years.
He lived with his wife, Morag in Buckie, the coastal town in Moray where he grew up.
It is not yet clear what caused Mr Flett’s death, but his employers have launched an investigation on the rig to try to find out what happened.
A spokesman for Transocean said: “We regret to confirm a fatality on board the drilling unit Transocean Rather.
“The fatality occured at approximately 9:10am local time on 13 April.
“A Transocean employee working as a ballast control operator was found without vital signs. The company has started an inquiry into the circumstances leading to the incident.”
Mr Flett and his wife were believed to have travelled to Dubai together last month before he went to work offshore.
His job would have involved making sure the rig was seaworthy and keeping the platform stabilised while drilling operations were ongoing.
Maintenance work was being carried out on the installation when Mr Flett died at the weekend.
The Transocean Rather is situated close to Labuan island, a remote area of Malaysia more than 1,000 miles from the country’s capital, Kuala Lumpur.
The 22,000-tonne rig was built in 1987 and can drill up to a depth of 25,000ft.
Transocean, an American-owned firm which was set up in the 1920s, now has offices in nearly 20 countries, including Angola, Nigeria and the Cayman Islands. The company owns a fleet of 79 mobile offshore drilling rigs, which are currently at points all around the world.
Councillor Gordon MacDonald, who is one of the representatives for the Buckie ward on Moray Council, said it was far too early to speculate on the cause of his death.
He added: “It’s a real tragedy that someone so young has died.
“Everyone’s feelings are with the family right now. My own youngest son works in the oil industry in that part of the world.
“Hearing this terribly sad news really does bring things home to you.”