A donation of £10m from Dame Stephanie Shirley has helped to launch the centre, which will be called the Oxford Internet Institute.
Public funds of £5m are also being used to open the centre, which it is hoped will put Britain at the forefront of e-research.
Oxford University said the centre would be the world's first multi-disciplinary institute and that it would carry out research and make policy recommendations on the effects of the internet on society.
It aims to put the institute, the UK and Europe at the centre of debates about how the web should be developed.
"Innovative institute"
The Education Secretary David Blunkett has welcomed the initiative: "I congratulate Oxford University on establishing this innovative institute."
"The effects of the internet are pervasive - through business, education and leisure.
"Britain needs a centre for top-class research on the difficult issues the Internet poses in cryptography, intellectual property rights, security and so on.
The institute will be based in Balliol College and academics say the subjects which could be studied include: Global law enforcement, regulation, privacy and security, e-democracy, and effects on education.
The Master-elect of Balliol, Andrew Graham, said the institute would perform a very important function.
"You can already shop, bank, vote, debate, argue, consult a doctor and get your degree over the net - and do so all around the globe," he said.
"However, there is also an enormous amount of rubbish out there and some material that is harmful.
"To understand what is happening and to formulate helpful policies you need people such as political scientists, lawyers, medics, economists and computing scientists working together.
"Building on the substantial strengths already in Oxford, this is what the Oxford Internet Institute will do," he said.
Dame Stephanie Shirley
Dame Stepanie Shirley made the £10m donation through The Shirley Foundation, which she set up.
She is the founder of FI Group, an IT services business.
Dame Stephanie, who is also known as Steve, said she was confident the institute would enable Britain to play a leading role in the research of social and ethical issues raised by the internet.
"These are global concerns and I am delighted that my funding has provided the Oxford Internet Institute with the firm foundation required to attract public, and in due course further private, financial backing," she said.
The £5m in public funding for the project has come from the Higher Education Funding Council for England, which is supported by the Department for Education.
Oxford University is already carrying out various research programmes and initiatives relating to the internet.