NatureScot, which approved the licence, said the decision marks the first ever conservation translocation of wildcats in the UK.
The Scottish Government agency said it hopes the project will help restore Scotland's critically-endangered wildcat population.
The Saving Wildcats partnership, which applied for the licence in September last year, plans to release around 20 wildcats annually, with the first trial release planned for June.
In considering the licence application, NatureScot assessed the proposed release site as suitable for relocating wildcats from the project's breeding centre at the Royal Zoological Society of Scotland's (RZSS) Highland Wildlife Park.
The agency, however, said while the project will benefit the species, there are risks and challenges associated with relocating predators and success will rely on the support of local communities.
NatureScot's head of biodiversity Dr Katherine Leys said: "Habitat loss, persecution and hybridisation with domestic cats has brought the Scottish wildcat population to the brink of extinction.
"The Saving Wildcats partnership has been a lifeline for the species and our decision to grant a translocation licence to allow wildcats to be released in the Highlands of Scotland marks a crucial point in the long journey towards conserving this iconic species.
"This journey is not without difficulty, and we know that there are more hurdles to overcome before we reach the point where we are ready to release the wildcats into carefully selected areas of the Cairngorms National Park.
"Once there, the wildcats will face further challenges, so it's crucial the project continues to work with local communities, farmers, land-owners and cat owners to ensure wildcats are given the best chance to survive and thrive."
Dr Helen Senn, the Saving Wildcats project lead and RZSS head of conservation, said the animals will be monitored using GPS collars following their release.
She said the chosen site provides "a suitable mix of habitats and potential prey for the species", adding: "It is fantastic to reach this milestone and press ahead with planning for trial wildcat releases in the Cairngorms over the summer."
Saving Wildcats is one of the largest species conservation projects in Britain and it is supported by RZSS, NatureScot, Forestry and Land Scotland and the Cairngorms National Park Authority, together with European partners Nordens Ark and Junta de Andalucia.
National Farmers Union Scotland’s policy manager Penny Middleton welcomed the news.
She said: “As a supporter of the official body, the Scottish Wildcat Action forum, we have previously helped disseminate information on how to protect this iconic native species to our members in the priority areas identified for wildcats, including the Cairngorms National Park area.
“We recognise that the species remains critically endangered and that the plans through the Saving Wildcats project to preserve the species are starting to come to fruition.
“The farming community in release areas will be keen to support these plans and identify how they can assist.”