However, there has been some concern at delays in signing the contract.
Deputy First Minister Nicola Sturgeon, who is also Govan MSP, welcomed the news.
She said: "Glasgow's shipyards are second to none and this contract recognises that valuable expertise.
"It is unfortunate that the shipyards and the workforce have faced significant delay from the Ministry of Defence in signing the contract, leading to some uncertainty at the yards, but this is a good day for shipbuilding on the Clyde and in Rosyth."
Liberal Democrat defence spokesman Willie Rennie, whose constituency includes Rosyth dockyard, said there had been "dithering and delay".
He added: "The Scottish and UK Governments must now ensure that the economic and employment opportunities these contracts provide for Scotland's shipbuilding industry are sustained far beyond the completion of these contracts."
Glasgow Chamber of Commerce chief executive Richard Cairns said: "This is fantastic news.
"Having recently been given a tour of the under-construction Type 45 destroyer HMS Dauntless, and being highly impressed by the skill and commitment of the staff at BAE Systems, I am certain these new carriers will be the best as well as the biggest."
HMS ELIZABETH AND HMS PRINCE OF WALES
Displacement: 65,000 tonnes
Length: 280m (920ft)
Width (at flight-deck level): 70m (230ft)
Keel to masthead: 56m (184ft)
Nine decks (plus flight deck)
Speed: 25+ knots
Range: 8,000-10,000 miles
Aircraft: 36 F-35 Joint Strike Fighters and four Airborne Early Warning aircraft, plus EH 101 Merlin helicopters
Crew: 1,450 (including air crew)
Weapons: Phalanx close-in weapon systems; 30mm and mini-guns
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