The company, led by Andrew and Scott Laing, alongside their father, Stewart, were given the go-ahead by Argyll and Bute Council.
Work is expected to start on Ardnahoe distillery in November, with production anticipated for early 2018.
Established in May 2013, Hunter Laing & Co currently distributes whisky to 65 markets around the world.
The new distillery will sit on a four-acre piece of land at Ardnahoe, on the north east coast of Islay, purchased from Islay Estates.
The distillery, the ninth on the island, will focus on creating a single malt Islay whisky and will be the first built since 2005.
The distillery will draw water from the nearby Ardnahoe Loch and production of around 200,000 litres of alcohol is planned for the first year.
Andrew Laing, director, said: "We are absolutely delighted that our plans for Ardnahoe
have been approved. Since starting our company, we’ve seen a huge demand for Islay whisky around the world and now is the perfect time to make the progression from blenders and bottlers to distillers and secure our own supply of Islay single malt."
Director Scott Laing said: "Our father spent time on Islay early in his career while working for a brief spell at Bruichladdich. He has always had a natural affinity with the island and we’re all fans of the peaty style of whisky it is renowned for so it’s wonderful to be able to build a distillery on the island."
The building of the distillery will see a visitor centre with a café, tasting room and shop. The distillery will create a range of full-time positions, as well as seasonal roles.
Laing, managing director, said: "This is the natural next step in the journey of Hunter Laing & Co. To be able to work with my sons on the new distillery is a real joy, as is the opportunity to be part of the incredible tradition of whisky-making on Islay, the whole experience is a dream come true."