Cornish people will be granted minority status under European rules for the protection of national minorities.
Chief Secretary to the Treasury Danny Alexander made the announcement on a visit to the county.
Dick Cole, leader of Mebyon Kernow, which campaigns for Cornish devolution, said: "This is a fantastic development. This is a proud day for Cornwall."
The Cornish will gain the same status as other Celtic communities the Scots, Welsh and Irish.
On a visit to Bodmin Mr Alexander said: "Cornish people have a proud history and a distinct identity.
"I am delighted that we have been able to officially recognise this and afford the Cornish people the same status as other minorities in the UK."
Mebyon Kernow leader Mr Cole said: "A lot of people have been working for many years to get Cornwall the recognition other Celtic people of the UK already receive.
"The detail is still to come out on what this might mean, but make no mistake that this is a proud day for Cornwall."
Bards from Gorsedh Kernow, which represents "the national Celtic spirit of Cornwall" welcomed the "historic announcement".
Grand Bard of Cornwall, Maureen Fuller, said: "Cornish people have a proud and distinct identity and a genuinely democratic society respects the ethnic, cultural and linguistic identity of people belonging to a national minority.
"We are proud of our history and our unique language and look forward to the day when these feature as regular subjects on school timetables and are spoken of by Cornish people as a way of life."
A group of key figures within Cornwall has been working on the paper setting out why the Cornish should be recognised by the Council of Europe's Framework Convention for the Protection of National Minorities.
Campaigner Bert Biscoe, an Independent councillor who is a member of the group, said: "I very much welcome that the Cornish as a group can stand equally beside all other groups in British society."
Cornwall Council leader John Pollard said: "There are obviously significant benefits for Cornwall in being included within the framework convention, which is worth celebrating, and I pay tribute to all those who have worked tirelessly over many years to achieve this status."
Cornwall in numbers
£75bn value of economy (0.6% of UK)
£22,087 average annual earnings (GB £26,551)
£1.1bn average annual tourism revenue
In the worst 5% of UK areas for households at risk of poverty
Key words in Cornish
How are you?
Yn poynt da (meur rasta)
Very well (thank you)
He said national minority status would not initially bring any additional funding or powers to the council or to Cornwall.
However, it does mean that Cornish people will be afforded the same protections as the Welsh, Scottish and the Irish; with government departments and public bodies required to take Cornwall's views into account when making decisions.
Communities Minister Stephen Williams added: "This is a great day for the people of Cornwall who have long campaigned for the distinctiveness and identity of the Cornish people to be recognised officially.
"The Cornish and Welsh are the oldest peoples on this island and as a proud Welshman I look forward to seeing St Piran's Flag flying with extra Celtic pride on 5 March next year."
Three previous attempts to include the Cornish in the Framework Convention had been unsuccessful, with the last made in 2011.
In March this year, Deputy Prime Minister Nick Clegg announced the government would be investing £120,000 into the Cornish Language Partnership to promote and develop the language.