Announcing the new figure in his annual oration to the university on 1 October, Professor Hamilton said that the retreat of the state from directly funding some aspects of higher education was "a trend that has caused a great deal of anger, sorrow, and soul-searching".
"Its wisdom is untested, certainly in this country, but its reality is undeniable," he said.
"With greater weight and reliance being placed upon the individual and the private, it is no surprise that the role and the importance of philanthropy is being drawn into ever sharper focus."
Professor Hamilton said that Oxford has already comfortably exceeded its original £1.25 billion target. But philanthropy was not "a magic bullet for the future funding of our universities, and nor is it a door through which the state can progressively leave the scene", he said.
"Governments can bring to bear resources on a scale that dwarfs every other funding stream, even the most generous philanthropic endowment."
He added that even in the US, where funding for some universities is thought to be largely private, most research income comes from the government - around 80 per cent at Harvard University, compared with around 40 per cent at Oxford.
Professor Hamilton said there was a risk that the "vital connective tissue" between the two beneficiaries of education - the individual and societies - would be "atrophied by a progressive withdrawal of public funding for universities, to the serious detriment of both".
During the speech, Professor Hamilton also announced that the fundraising drive would pay for a £100 million matched funding scheme for postgraduate scholarships, starting in 2013-14, in an effort to close what he called the "graduate funding gap".
Under the scheme, open to applicants in all master's and doctoral courses, scholarships will be awarded based on academic merit and will cover the full costs of fees and living expenses.
The institution plans for 60 per cent of the money to come from philanthropic donors while it makes up the remainder.
Oxford already runs extensive scholarship schemes, funded through donations, for undergraduates from low-income families, postgraduate students in the humanities and at the new Blavatnik School of Government.