The new system means orders can be placed anytime and the technology has been programmed to give first-time buyers an advantage over regular customers.
The beers must be picked up from the abbey in West Flanders. Every beer and every shopper will have an online code, which means customers can be linked to the beers they buy.
No customer can return until 60 days after their last purchase, a ruling that was enforced under the old system by the monks demanding the registration plate of their visitors' cars.
Would-be customers previously had to call the extremely busy hotline at a given time and pray their call was answered.
If they were lucky enough to get through, they could place an order for a maximum of two crates of beer and reserve a time to pick them up.
“We like to give as many people as possible the opportunity to buy our beer at the right price,” Brother Manu Van Hecke, Abbot of St Sixtus Abbey, told Flemish broadcaster VRT.
“Anyone who does not adhere to the sales rules and abuses the system will be denied access to the web store."
The brewing brothers of Belgium’s St Sixtus Abbey have been forced to go digital in a bid to stop the thriving black market in the “Holy Grail” of beers.
Westvleteren 12 is considered by some experts to be the best beer in the world and is highly sought after. In Brussels a bottle can sell for about £14, £40 in the US, while in Dubai prices can reach £240.
Its cachet is increased by the Trappist monks’ resolve to only brew as much each year as they need to cover their annual costs, and the strict rules governing the sale of the 10.2 per cent dark beer.
“We brew to live, we do not live to brew,” is the monks’ motto. The brothers sell a crate of 24 bottles for £40 and insist the beers should only be sold to private individuals and not businesses.
Despite the ban, it is possible to buy Westvleteren, which has been brewed since 1838, in some off-licences and bars at inflated prices in Belgium.
Last year, a Dutch supermarket chain earned a stern rebuke from the monks after putting 7,000 bottles on sale at £9 a bottle.
That scandal prompted the monks to abandon the complicated phone ordering system they have used for the last 15 years in favour of an online shop.