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.
A £3.2m supercomputer, one of the most powerful in the UK, has been installed at the University of Southampton.