Bruichladdich, sold in a £58 million deal to luxury drinks company Remy Cointreau in July, said the move was needed to provide enough supply to feed the distribution network of its new French owner and keep up with demand.
It comes as the Ardbeg distillery on the opposite side of the island moves to 24/7 production in the new year following its acquisition by luxury brands conglomerate Louis Vuitton Moet Hennessy (LVMH).
Carl Reavey, spokesman for Bruichladdich, said: "We currently produce about 700 to 750,000 litres a year but we are intending to go to maximum production of 1.5 million litres.
"That is without changing any of our production methods.
"We have been the bootstrap boys of small independent distillers and we have had to hustle and bustle our way around the world so the scale of this is incredible.
"Remy as a company is 100 times bigger that Bruichladdich and it has a distribution network to match.
"The only way we can even possibly begin to meet what Remy is going to require from us is to increase production.
Mr Reavey said more warehouses would be required to house the growing stocks and, while numbers were yet to be confirmed, extra staff would be essential to the company's growth.
He added: "Going forward it is all very positive for us and it is very exciting times at Bruichladdich.
"Remy are really, really keen on us being even more independently minded and challenging, rather than us becoming just another Scotch whisky distiller.
"It is nice to see how committed they are to Islay, to the things we really hold dear here. They really get that."
Barley used in Bruichladdich is grown at 10 farms on the island, and there are hopes of increasing the homegrown product, which accounts for 45% of the grain used in the malt.
The remaining barley, at present, comes from the Black Isle.
Mr Reavey added: "We're so Islay-obsessed that we want everything to be done here."
Bruichladdich was revived in 2000 by Mark Reynier from a mothballed distillery that sat largely dormant for six years, bar a handful of test productions.
Under the leadership of Mr Reynier, it became the largest private-sector employer on Islay with 50 members of staff.
Following its sale to Remy Cointreau, thought to be the largest transaction ever involving a single whisky distillery, shareholders received windfalls equivalent to more than seven times their initial investment.
Whisky industry analyst Alan Gray, of Sutherlands Edinburgh, said the French had become a major player in the Scottish marketplace, with Pernod Ricard also producing Ballantine's, Chivas Regal and Glenlivet.
France was also number one for total value of sales in 2011, with a surge in buying partly driven by the country's increase in tax on Scotch whisky that came into force in January 2012.
Overall, Mr Gray said sales volumes in the first nine months of 2012 were down 7.4% on the year, with sales values down 1.2% given price rises driven by increased demand and the shortened supply created by the shifting of excess stocks traditionally held by most distilleries.
He added that the dip in sales should be seen in the context of a record 2011, with the industry enjoying a very strong two years.
Mr Gray added: "It is fair to say that Islay, as a whole category, is doing very well.
"The arrival of Remy Cointreau shows it is confident in the future of the whisky industry and Bruichladdich itself.
"In the case of LVMH, which is very, very big internationally, it indicates that Ardbeg is poised to do very well."
Jackie Thomson, visitor centre manager at Ardbeg, said demand for its 10-year-old had gone "through the roof".
She said: "It has taken a while for it to get on the map as for a long time it wasn't being made as a single malt, it was going into blends.
"But now to insatiate the demand coming through from Norway, the US and Eastern Europe we are going to seven-day production and have taken on give more production staff."
She said things had not always been so simple for the distillery. "Ardbeg closed in 1981 and again in 1989 but even before then production was sporadic both before and after the time it was closed," she said.
"It was owned by a number of firms who never had a grand plan and they didn't lay down stocks for single malts. It became a victim of its own success."
Ardbeg will now move from producing 700,000 litres a year to more than 1.1 million litres.
It will retain just two stills but move from eight to 14 mashings, where the malted barley is mixed and heated with water, a day.