Few people would connect the drab olive green of an Israeli army uniform with the cutting edge of fashion. And most fans of Stylit, a website where a virtual personal stylist matches clothes and accessories to suit your taste, are unaware that it uses technology adapted from algorithms originally developed to track and prevent suicide bombings.

Stylit was one of 19 young tech companies displaying their wares in Tel Aviv recently at the end of a five-month entrepreneurship programme run by alumni of an Israeli intelligence unit that has spawned more tech millionaires than many business schools.

Similar to Britain's GCHQ, Unit 8200 manages Israel's army signals intelligence, sucking in and analysing vast amounts of electronic data, from wiretapped phone calls and emails to microwave and satellite broadcasts. On the new hi-tech battlefield, 8200 is now the largest unit in the Israel Defence Forces (IDF).

Demobbed geeks once overshadowed by gun-toting commandos have made the most of their expertise in cybersecurity, data storage, mobile communications and analytical algorithms to help transform the basis of Israel's economy from orange groves to mobile-phone apps. Israeli inventions include instant messaging, the USB memory stick, the firewall and the secure data links that enable most of the world's banking transactions and TV signal decoders.

Israeli tech firms Nice, Comverse and Check Point were all created by 8200 alumni or based on technology originally developed by the unit. With the emergence of consumer apps based on crunching vast amounts of information known as "big data", Israel is a decade ahead of the US and Europe – and all because of the military.

New startups such as Stylit hope to emulate the success of Waze, a big-data-based driving app developed by former IDF cyber-squaddies and bought by Google for more than $1bn (£654m).

"A lot of the practices and the technology that we used in the army are used today at Stylit to address the problems we are aiming to solve in fashion," said Yaniv Nissim, a former 8200 programmer who designed the company's algorithm by combining the wisdom of former army tech geeks with fashion industry stylists.

"The technology is mainly machine-learning technology. It's how to take huge amounts of information and from that to understand users' behaviour."

Big data predictive algorithms developed to prevent enemy attacks also power Any.Do, one of the world's most popular productivity apps for mobile devices. For Nissim's army buddies, 8200 is Israeli hi-tech's old school tie, opening doors to a vast group of like-minded and similarly-trained entrepreneurs. Rompr is a mobile app through which parents can share information about activities for toddlers. Chief executive Noa Levy and the three co-founders all served in elite IDF tech units.

"Trying to make sense of the patterns you find when you study a lot of data and turning that into actionable information – that's the guiding principle that we have in Rompr and also something that is very important in those technological units," she says.

"It's more the mindset than the actual technology. Then you can go out and do it on a completely different series of tasks, using the same methodology."

Until a decade ago, Unit 8200 was a secret. Then it starred in the book Start-Up Nation, which chronicled Israel's emergence as a hi-tech powerhouse with more venture capital investment per person than anywhere in the world and the largest number of Nasdaq-listed companies after the US and China. Three years ago, 8200 alumni decided to emerge from the shadows and offer their expertise to other young Israeli entrepreneurs.

The result was the 8200 entrepreneurship and innovation support program (EISP), a five-month hi-tech incubator in which unit alumni volunteer to mentor early-stage startups. So far, 22 of them have received funding totalling $21m (£13.5m) and employ 200 people, joining the 230,000 employees of Israel's 5,000 tech companies that earn $25bn a year – a quarter of Israel's total exports.

Nir Lempert, a reserve colonel, former deputy commander of Unit 8200 and chairman of its alumni association, says the unit handpicks the brightest teenagers in the country then trains them to solve problems in multidisciplinary teams using methods usually associated with business, not battles. They are encouraged to think differently. "The central mission of the unit is to save lives, to prevent terror and other attacks," says Lempert. "We teach our people that the mission is so important that there is no possibility of failure."

The 8200 legend attracts increasing numbers of young Israelis into IDF tech units. Mamram, the main IT support unit of the IDF, now offers a six-month pre-army course at its headquarters base in a suburban street on the outskirts of Tel Aviv. From dawn into the night, recruits study programming skills, teamwork, project management and – most important – how to be creative. It's the ultimate startup boot camp.