Glasgow is to benefit from an additional £24m in government funding to boost science and technology.
Willetts said that the money would go towards making Glasgow "a model of what a future city could look like and how it could run".
Glasgow City Council won the funding through the Technology Strategy Board after a competition with other cities around the UK to become a "large-scale demonstrator" of future technologies for urban living.
The money will go towards projects to improve transport and mobility, promote healthy living, address community safety and fear of crime, and enhance energy efficiency. Willetts said that the cash would allow Glasgow to trial technologies and systems which would later be adopted by cities in Britain and around the world.
He told BBC Radio 4's 'Today' programme: "Where Glasgow leads, the rest of the country follows, and I think the rest of the world follows. This is about what is going to happen in Sao Paulo and Lagos. These are export opportunities."
Willetts told BBC Radio Scotland how the plan for the future would work. "What it really means is high-tech cities where all the information that's currently spread around in different systems is properly brought together, information about how much energy we're using, where the energy use is coming from, the flow of traffic, the health pressures. One of the biggest things happening in the world at the moment is a big influx of people into cities.
"Glasgow has won this competition, £24m of investment, because we want Glasgow to be a world-class demonstrator of how you can collect all this information in a very high-tech way, bring it together and manage your city better. We think that's going to be good for Glasgow and it's going to be good for the economy as a whole."
Willetts told the 'Good Morning Scotland' programme that Glasgow was chosen because of the "innovative thinking" going on in the city.
"There's also a massive amount of investment going into Glasgow," he added. "We reckon there's about £2bn coming in with the Commonwealth Games."
He went on: "Britain was the first country in the world where more than half of the population lived in cities. Now that's just happened across the globe as a whole.
"Imagine our government being a world leader in urban planning and urban living."
News that Glasgow has won the competition was welcomed by the Scottish government. Deputy First Minister Nicola Sturgeon said: "Generations of talented Scots have helped cement Glasgow's global reputation for innovation and creativity, and I am delighted the city has won its bid to secure the £24m Future Cities demonstrator.
"The Scottish government recognises the importance of capitalising on Scotland's strengths and this investment reinforces our reputation as a dynamic and innovative nation. Not only is this really positive for Glasgow, it also provides a great opportunity for other Scottish cities to benefit through the collaborative working of the Scottish Cities Alliance."
Iain Gray, chief executive of the Technology Strategy Board, said: “The global market for innovative approaches to delivering efficient, attractive and resilient cities is growing, and UK companies – supported by our world-class academic and research base – are well-positioned to exploit it.
"This large-scale demonstrator will show just what can be achieved by innovative use of today’s technology, and will help UK companies develop solutions and technologies for the future, for the benefit of the UK economy.”
The large-scale demonstrator will be made up of a series of projects that will improve transport and mobility across the city.
It will develop programmes to promote healthy living, deliver advanced street lighting to address community safety and perception of crime, and enhance building energy efficiency to provide affordable warmth.
Value will be created by capturing and opening up data, improving the city’s real-time operations with a city dashboard and a management system that views the city as an integrated whole, and a ‘MyGlasgow’ public window on the city to deliver multiple benefits for the people of Glasgow.