The Institute aims to position the country as a world leader in the analysis and application of big data and algorithm research. Its headquarters will be based at the British Library.
Cable said: "Headed by the universities of Cambridge, Edinburgh, Oxford, Warwick and UCL (University College London) the Alan Turing Institute will attract the best data scientists and mathematicians from the UK and across the globe, to break new boundaries in how we use big data in a fast moving, competitive world."
The delivery of the Institute is being coordinated by the Engineering and Physical Sciences Research Council (EPSRC), which invests in research and postgraduate training across the UK. The Institute is being funded over five years with £42 million from the UK government.
The selected university partners will contribute further funding. In addition, the Institute will seek to partner with other business and government bodies.
Professor Philip Nelson, EPSRC chief executive, said: "The Alan Turing Institute will draw on the best of the best academic talent in the country. It will use the power of mathematics, statistics and computer science to analyse big data in many ways, including the ability to improve online security.
"Big data is going to play a central role in how we run our industries, businesses and services. Economies that invest in research are more likely to be strong and resilient."