Energy regulator Ofgem announced it has approved the link, which will see more than 100 miles of subsea and underground cables laid in the Moray Firth.
At the same time it also announced plans to cut charges for green energy generators.
Ofgem said that from April 1 2016, charges to these suppliers from the transmission operator, National Grid, will more closely reflect their use of the network.
The watchdog said this would benefit suppliers of wind or solar energy who do not constantly use the grid.
First Minister Alex Salmond said both announcements are “welcome news for the Scottish electricity sector and consumers”.
He added: “They support the transition to a low-carbon economy by encouraging renewable generation in the areas of highest resource and ensure Scotland continues to play a vital role in delivering security of electricity supply across these islands.”
The subsea cable aims to connect 1.2 gigawatts of renewable energy - enough to power the equivalent of almost 640,000 homes - with the grid.
The scheme, which is due to be completed in 2018, represents the largest investment in the region’s electricity network since the hydro era of the 1950s.
Work on the project, which is being led by SSE subsidiary Scottish Hydro Electricity Transmission, is expected to begin in the next few months, with more than 600 jobs being created.
Mark Mathieson, managing director of networks at the energy company, said it had worked hard to ensure “we have the best solution for connecting renewable energy to the transmission system”.
He added: “’I am very pleased that it has been given the green light and we will now work with Ofgem on the remaining details and focus on ensuring that the new link is constructed in a safe and responsible way so that the benefits it will bring in unlocking renewable sources of energy for decades to come are realised.’’
Mr Salmond said: “The £1.2 billion investment by Scottish Hydro Electric Transmission will ensure continued progress towards our renewable energy ambitions, play a role in supporting future island generation and support hundreds of jobs during construction. It also underlines once again the essential role that renewable energy in Scotland has to play in meeting the UK’s long-term energy requirements.”
He also said that Ofgem’s decision to “reduce the level of discriminatory grid charges for electricity generators in Scotland is particularly welcome”.
Ofgem senior partner for transmission Martin Crouch said the new subsea cable is a “major step forward for an essential upgrade to the high voltage grid so that more renewable energy can connect to the networks”.
He added that the changes to the transmission charging regime are “the result of an extensive consultation process and detailed analysis”, and said: “The new arrangements more accurately reflect the costs of Britain’s diverse energy generation and will lead to lower costs overall for consumers.’’
Michael Rieley, senior policy manager at the industry body Scottish Renewables, said the subsea link would “significantly reduce bottlenecks on the system, and could unleash over 1.2GW of renewable energy projects in the north of Scotland which is enough energy to power the equivalent of 637,575 homes”.
Mr Rieley added changes to the charging regime are “a long-awaited, and much welcomed, recognition of the value of the Scottish renewable energy sector”.
He said: “The changes will help create a more level playing field between generators on the Scottish mainland and those further south, which is crucial if we are to make the transition to a low-carbon energy system while also providing value for consumers.
“Despite our disappointment that the new charging regime won’t be implemented until 2016, four years later than originally estimated, this announcement from Ofgem is undoubtedly good news for the sector.”
Lang Banks, director of environmental body WWF Scotland, said: “Given the urgent need to clean up the UK’s power sector, cut climate emissions and keep the lights on, it’s bizarre we’ve had a system in place that has effectively penalised some of the nation’s best locations for generating renewable energy.
“While it’s a pity that the scheme won’t now start until 2016, we very much welcome the news that an agreement has been reached to improve the electricity charging regime. This decision should help to unlock much more of Scotland’s massive renewable energy potential.
“Scotland already generates about a third of the UK’s entire renewable electricity needs and has the potential to contribute more in the future now that this agreement is in place.”