The UK supermajor also announced that it has struck a significant new hydrocarbons column at an appraisal well elsewhere on the Clair field.
The government approval for Clair Ridge is part of a wider £10 billion ($15.75 billion) investment in the UK North Sea over the next five years by BP and its partners including Shell, Chevron and ConocoPhillips.
Total investment for the Clair Ridge project west of the Shetland Islands is £4.5 billion. It will involve the construction and installation of two new bridge-linked platforms which are set to be installed in 2015 before coming on stream the following year.
"The new development will have the capability to produce an estimated 640 million barrels of oil and will provide a hub for future expansion, subject to further appraisal. Peak production is expected to be up to 120,000 barrels of oil per day," BP wrote in a statement announcing the approval on Thursday morning.
The Clair Ridge development will extend production from the Clair field up to 2050.
British Prime Minister David Cameron, who is due to meet oil and gas representatives in Aberdeen today, commented: “I am delighted to give the go-ahead for this project; this investment is great news for Aberdeen and the country and provides a massive boost for jobs and growth.
"It shows the confidence that there is to invest in the North Sea – we have cutting edge technology, world class skills and expertise and a UK Government that is committed to do what we can to secure future investment.”
BP's boss of North Sea business Trevor Garlick said: “The Clair field is an established, high quality asset with a strong future and with our co-venturers we are taking significant steps to maximise its potential.”
Clair Ridge is one of four BP-operated projects which together are to see an investment of £10 billion over the next five years, BP's portion of which is £4 billion.
"Over half of the total investment in the projects is expected to be spent in the UK. At their peak, taken together, the projects will provide some 3000 UK oil and gas supply chain jobs, and will play a major part in sustaining the more than 3500 jobs already existing in BP’s North Sea operations," BP's statement read.
BP also revealed that an appraisal well at South West Clair had hit "a significant new hydrocarbon column in an overlying reservoir horizon, which is expected to support further development of the greater Clair field area in the future".
Commenting on the raft of new investments, BP chief executive Bob Dudley said: “After some years of decline, we now see the potential to maintain our production from the North Sea at around 200,000–250,000 barrels of oil equivalent a day until 2030. And we are working on projects that will take production from some of our largest fields out towards 2050.”