High Performance Computing (HPC) Wales will provide computers that can handle and analyse massive amounts of data at a high speed.
The assembly government said it will help the economy by encouraging world-class research and development.
Researchers have welcomed the project.
The new technology will mean that tasks that usually take months using normal computers can be done in days or even minutes.
It can be used for many diverse tasks, such as facial reconstruction modelling, animated graphics, nuclear energy research, petroleum exploration, car crash simulations and airflows over aircraft wings.
The assembly government, which is helping to fund the technology, said it will give Wales a super-computing capacity and network at a scale not attempted anywhere else in the UK or Europe, which will help the country's economy and business competitiveness.
It will also help create over 400 jobs in industry, it added.
"The scale of this project is ambitious and will reach all four corners of Wales," said Lesley Griffiths, deputy minister for science, innovation and skills in the assembly government.
DEMENTIA STUDY, BANGOR UNIVERSITY- Teams are working on different brain images to try to understand pain and dementia and how to protect against further deterioration of the brain. HPC will help analyse the data.
ENVIRONMENTAL STUDY, ABERYSTWYTH UNIVERSITY - Scientists have developed computer software applications that analyse satellite image data to monitor environmental impact and change. HPC will speed up the process and help environmental initiatives and businesses.
HYDROCARBON EXPLORATION, CARDIFF UNIVERSITY - Researchers are trying to better understand plate motion history and the role of the Earth's mantle. Scientists are starting to create models of the history of plate motion going back 80 million years. Plate models dating further back need HPC to help work out if they are correct and realistic.
Source: Welsh Assembly Government
"It will speed up innovation from research carried out in Welsh universities through to commercial market ready products."
The main computer hubs for HPC Wales will be in Cardiff and Swansea, with links to Aberystwyth, Bangor and Glamorgan universities, along with University of Wales Alliance Universities and Technium business innovation centres around Wales.
More than 100 innovation collaborative projects between the universities and industry in Wales have already been identified that would benefit from HPC technology.
These range from modelling and simulating medical implants to analysing satellite images for monitoring environmental change.
Professor Ian Cluckie, Swansea University's pro vice chancellor for science and engineering, said the new technology would help researchers and businesses across Wales.
He said: "It will ensure that researchers, students and businesses have access to state-of-the-art high performance computing, that is required to undertake the internationally recognised research that drives the knowledge economy and underpins the Welsh agenda in crucial sectors such as health, science, engineering and advanced manufacturing."
Professor Noel Lloyd, chair of Higher Education Wales and vice chancellor of Aberystwyth University, added: "This is tremendous for Wales, both in terms of research capacity and the ways in which the higher education sector can work in collaboration to provide opportunities and training for business."
The assembly government is putting £24m into the five year project, including money from the EU Convergence programmes and £10m from the UK Department for Business, Innovation and Skills.
Funding will also come from collaborating institutions and private and research income.

The south coast side have never featured in the last eight and will now host eight-time winners Liverpool at the Goldsands Stadium.
Derby have a home tie against Premier League leaders Chelsea, while League One Sheffield United welcome high-flying Southampton.
Newcastle, who knocked out holders Manchester City, travel to Tottenham.
The ties will be played in the week beginning 15 December.
Sheffield United reached the semi-finals of the FA Cup last season and are enjoying another good cup run after knocking out MK Dons in the previous round.
Championship leaders Derby are rewarded for coming from 2-0 down to beat Fulham 5-2 with a home draw against the Premier League leaders.
Bournemouth - the third of the non-Premier League sides left in the competition - eliminated West Brom on Tuesday.
Full quarter-final draw:
Derby v Chelsea
Tottenham v Newcastle
Bournemouth v Liverpool
Sheffield United v Southampton
A £40m super computer project has been launched that will give businesses and universities in Wales access to the most advanced computing technology currently available.
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Championship side Bournemouth will play Liverpool in the quarter-finals of the Capital One Cup.