Kenneth Whiteside, 59, was one of two Scots believed to have been killed at In Amenas. His brother Bob, from Crieff in Perthshire, said the family learned of his death through Facebook.
Carson Bilsland, from Perthshire, has been named locally as the other Scot feared dead. Friends said his family had been told he was believed to be among the fatalities.
Another Scottish man, Barry Lawson, from St Andrews, had been unaccounted for but has been confirmed as safe, according to reports.
David Cameron updated MPs on the attack yesterday, warning the world must confront the growing terrorist threat in North Africa and saying the region was “becoming a magnet for jihadists from other countries who share this poisonous ideology”.
The Prime Minister said the UK would provide intelligence and counter-terrorism assets to help an international effort to track down and dismantle the network responsible for the attack.
He added that bringing home the victims’ bodies would be a priority.
Algerian prime minister Abdelmalek Sellal said 38 hostages, 37 of whom were foreign, had been killed, along with 29 militants.
Three Britons have been confirmed among the fatalities, with three more missing and believed to be dead.
Mr Whiteside was originally from Glenrothes, in Fife, but is understood to have emigrated many years ago to South Africa, where he lived in Johannesburg with his wife and two daughters. He had been working in Algeria for about five years. He was a planning manager at the In Amenas desert complex and was among 800 employees, including 135 foreigners, working there when terrorists stormed the site last Wednesday.
“We know now what’s happened to Kenny, but we actually had to find out for ourselves,” his brother said yesterday.
“We were not given any official information and it was through Facebook, of all things, that we found out of Kenny’s demise. It was my daughter who found it on Facebook, a message from an Algerian co-worker.
“The police came last night and informed us that what was on Facebook was true, that Kenny had been … he was executed.”
He added: “I don’t hold any grudges against the Algerian army or anything, because that’s the way they work, that’s their system and they weren’t bothered about the hostages as such, they just wanted to get the camp cleared of all the terrorists.
“That was their main objective, as far as I can see.”
Mr Whiteside said of his brother: “He’s worked all over Africa and all over Russia. He’s been around. He knew what the game was all about.”
A survivor of the hostage crisis last night paid tribute to Mr Whiteside and Mr Bilsland.
Peter Hunter, 53, from Durham, who was reunited with wife Kerry yesterday after he spent days in hiding at a secret location at the sprawling plant, said he was “fortunate” to be able to return home and described the two Scots as “lovely guys”.
He said: “I guess you could say I was not in the wrong place at the wrong time. I used to see Carson every morning and every lunchtime, and we always had a bit of banter. He was a lovely guy, they all were.
“Kenny Whiteside used to play the bagpipes. Occasionally, he would have his kilt on. I used to sit on the step there and he used to say, ‘I do requests’. He was a lovely, lovely man. It’s just very sad.”
Friends of Mr Bilsland, 46, said he was a “true gentleman” with “a taste for adventure”. A friend of his father, Ian, said: “Carson worked away a lot and had done for years, just because of the nature of his work. He had been in Algeria for nearly two years.
“He had worked out in Africa before and I think some of the time the conditions can be a bit hairy, but no-one could have foreseen something like this happening.
“It’s horrific to think all of these innocent people have been murdered just to make a political point. It’s barbaric.
“I know the family will be absolutely distraught.
“Carson, like his dad, was a true gentleman. I know he was a really keen diver and he had a bit of a taste for adventure.”
Mr Bilsland had been working as a non-destructive testing technician at the plant, which is jointly operated by BP, Norwegian firm Statoil and local company Sonatrach.
He had previously worked as a skiing instructor at Glenshee, in Cairngorm national park, and was a former member of the British speed skiing team.
A spokesman for the team said: “It is a very sad day for British speed skiing.
“He was a hostage until the end when the Algerian special forces stormed a workshop with their no-negotiation strategy.
“I’m sure he wouldn’t have given an inch. Carson was one of life’s indomitable characters. He will be sorely missed but very fondly remembered.”
Former skiing colleague Murray Gordon said: “He was always up for a laugh and enjoyed his skiing. He was a very popular instructor and just a really nice guy.
“Obviously, he moved on from skiing and into the oil industry, and I understand he was really enjoying that.”
Perthshire North MSP John Swinney wrote on Twitter: “Deeply saddened that one of my constituents has not survived the Algerian hostage incident. My thoughts to his family at this terrible time.”
A Colombian-born UK resident is also believed to have died in the attack.
Japanese officials said they have lost seven nationals, with three more missing, while three Americans also died. Workers from Norway, Romania, the Philippines and Malaysia are also believed to have been killed.
The terrorists included men from Canada, Egypt, Mali, Niger, Mauritania and Tunisia, as well as three Algerians.
Justice secretary Kenny Mac-Askill said the hostages had been through a “horrendous ordeal”. He said: “We know that eight got back safe and sound [to Scotland], and are now back with their families, apart from one who, I think, decided to stop off with friends in London.
“But we do believe that two Scots, or those with an immediate family connection in Scotland, are believed to be among the missing, presumed dead.
“As the victims who have survived come home, they will be in contact to see what counselling can be provided, because even those who have survived have been through an horrendous ordeal, as we have seen on the television, and we will be making sure, through police and other agencies, that appropriate contact is provided.”
Evidence emerged yesterday that the Islamic militants who lay siege to the gas plant might have had inside help for what was a carefully planned attack.
They wore Algerian army uniforms, memorised the layout, included a former worker with detailed knowledge of the plant and had team of explosives experts ready to blow the place up, according to the Algerian premier, Mr Sellal.
He said three of the attackers had been captured and five foreign workers remained unaccounted for. He went on: “You may have heard the last words of the terrorist chief.
“He gave the order for all the foreigners to be killed, so there was a mass execution – many hostages were killed by a bullet to the head.”