The shipyard in Rosyth – which is run by defence giant Babcock – is also one of the final two bidders for a Swedish navy contract for up to seven of the same Type 31 ships, the BBC reports.
Competition for the Swedish contract is with a French shipbuilding firm, which has the support of the French government.
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The contracts have been in discussion for more than a year and decisions are expected within the next six months.
It comes after BAE Systems, which runs military shipyards on the Clyde at Scotstoun and Govan, secured a contract to build Type 26 frigates for the Royal Norwegian Navy.
First Minister John Swinney celebrated the “welcome investment”, saying it demonstrates “the strength of the skills within Scotland”.
And Prime Minister Keir Starmer visited the Govan shipyard on Thursday to welcome the news, after previously falsely claiming that his SNP counterpart had failed to comment on the deal.
The smaller, less-sophisticated and less expensive Type 31 is a “general purpose” fighting ship – also known to the Babcock team selling the design around the world as Arrowhead 140.
At 455ft (139m) in length and at 5700 tonnes, it is based on a design already in use with the Danish navy.
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Babcock’s director of the Type 31 programme, former Second Sea Lord in the Royal Navy, Admiral Sir Nick Hine, said the priorities for buying ships has long been “performance, cost and timing” and that has now been reversed.
He said: “It’s the ship that navies need. It’s affordable and adaptable and we can deliver it in 10 years. That’s never been done before.
“The future for Rosyth looks really good.”
Babcock said that the current Rosyth workforce of 2500 could rise to 4000 if it is successful in winning the Danish and Swedish bids, along with its other work in maintenance of the Royal Navy’s aircraft carriers.
