The Iridis4 has state of the art coprocessors which can each perform a trillion calculations per second - a measurement known as a "teraflop".
The university said the new machine would allow academics to work on more projects at faster speeds.
Iridis4 will be used for subjects such as engineering, archaeology and medicine, as well as computer science.
Pro vice-chancellor Prof Philip Nelson said: "Staying ahead of the game in high performance computing [HPC] is vital to help the university stay competitive.
"Simulation and computation enabled by HPC are recognised globally as the third pillar of modern research and this investment will ensure we remain world leaders in this field."
Iridis4 will be used for a range of research, including engineering, archaeology and medicine, as well as computer science.
The world's most powerful computer is China's Tianhe-2, which can perform 33,860 trillion calculations per second.
The university said its new computer ranked among the top 10 in the UK.
The most powerful is at the Science and Technology Facilities Council in Warrington.
Others are based at the University of Edinburgh, the European Centre for Medium-Range Weather Forecasts and the United Kingdom Meteorological Office.

However, 43% of the people asked said they did believe in the resurrection - although many did not think it happened as described in the Bible.
The figures found while 57% classified themselves as Christian, fewer than 10% read the Bible and prayed regularly, or go to church at least once a month.
The Church of England's General Synod will discuss the survey in November.
The survey of more than 4,000 people was commissioned by the Church, Hope - which represents churches of all denominations - and the Evangelical Alliance - which represents evangelical Christians in the UK.
Many scholars agree that Jesus was a real man, who lived in Galilee more than 2,000 years ago, although many details surrounding his life are still debated.
But, the Church of England survey found that four in 10 people did not believe Jesus was a real person, with a quarter of 18 to 34 year olds believing he was a mythical or fictional character.
The poll was part of a wider research project looking at both practising Christians and the wider population.
After Christians, the second biggest group identified in the poll - 12% - were atheists, while 9% were agnostics, Muslims represented 3%, with Hindus and Jews both making up 2%.
English Christians are more likely than the average English adult to work in education, or professional jobs, but less likely to work in finance or insurance, the survey concluded.

The 26-year-old has made 54 competitive appearances for the Cherry and Whites since arriving in 2014.
A former Sale Sharks, Wasps and Bedford Blues player, Atkinson has started a total of 21 Premiership matches.
"It's been great to get game-time this season. I'm excited to get this run of games and really push on," he told Gloucester's club website.
Director of rugby David Humphreys added: "Mark is someone who has been a stand-out performer every time he takes to the field."
A £3.2m supercomputer, one of the most powerful in the UK, has been installed at the University of Southampton.
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Forty percent of people in England do not believe Jesus was a real person, a Church of England survey suggests.
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Gloucester centre Mark Atkinson has agreed a new "long-term" contract with the Premiership club.