A former wave power plant in Leith Docks will play host to the six-part series, The Rig, which will be filmed exclusively in Scotland.
Due to start filming next year, it will follow the crew of a North Sea oil rig who are due to return to the mainland when an eerie fog descends and a mysterious force begins to take hold.
The Rig, which is being created by Scottish writer David MacPherson, will be the first major production to be made in Scotland by Amazon Prime, which says it plans to launch the series exclusively in 240 countries and territories.
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Some scenes in The Rig, which will be produced by Wild Mercury, makers of the Channel 4 drama Humans and the BBC-Netflix show Troy: Fall of a City, are expected to be shot on a real-life oil rig.
The Rig will take over the former Pelamis building in Leith Docks, which Connery, an award-winning actor and director in his own right, and producer Bob Last secured earlier this year under a £1 million deal with the Scottish Government to get it off the ground. It was previously used for the blockbuster Avengers: Infinity War.
Government agency Screen Scotland predicted their First Stage Studios would “raise the visibility of Scotland on screen, anchor more film and high-end television productions in Scotland and capitalise on the global boom in the industry.”
Amazon Prime’s official announcement said: “The Rig follows the crew of the Kishorn Bravo oil rig, stationed off the Scottish coast in the dangerous waters of the North Sea.
"When the crew are due to return to the mainland, a mysterious and all-enveloping fog rolls through and they find themselves cut off from all communication with the shore and the outside world.
"As they endeavour to discover what’s driving this force, bonds are broken, allegiances formed and generational fault lines exposed.
"The crew will be driven to the limits of both their loyalties and their endurance, into a confrontation with forces beyond their imagination.
MacPherson told this Twitter followers: “Massive thanks to the teams at Wild Mercury and Amazon Prime for believing in my vision for the show. We've crafted a great team for the show.
"We can't wait to take you to one of the harshest environments on Earth for an action packed story that pushes to the absolute limits. You won't have seen anything like this before!”
Georgia Brown, director of European Amazing Originals for Amazon Prime Video, said: “The Rig is a brilliant story, expertly told, in the most dramatic of settings.
"It asks searching questions about nature and the environment, about what it takes to survive and to be human, which feels very pertinent to the world we are living in now.”
Derek Wax, managing director of Wild Mercury said; “The Rig is a character-driven, epic thriller, full of heart-grabbing action and bold, original ideas.
“David MacPherson captures life on a North Sea oil rig with extraordinary authenticity and it’s been exciting to work with him, director John Strickland and our creative team in realising the scale and vision of this world.”