The Act of Parliament constituting the University provided that a 'Senate' should be elected as soon as the number of graduates who attained degrees above the rank of bachelor reached one hundred. The required number was reached in 1867, though for a time a majority of these were graduates of other universities who had been admitted to higher degrees at Melbourne ad eundem. It was not until 1881 that the University of Melbourne could claim one hundred full alumni.
The Senate had the right to elect members to Council and to reject or accept legislation framed by it, but not to frame statutes. Its role was not to duplicate the executive and administrative functions of Council but to act as a body of review. This was a somewhat 'unwieldy bi-cameral structure' and the Senate could and did, under certain conditions, exert considerable influence over the governance of the University. It was also important in maintaining an intimate connection between the graduates and the University thus enhancing its capacity to draw on their support as they progressed through their careers.
At the first meeting of the Senate in July 1867, Dr J.E. Bromby, head master of the Melbourne Church of England Grammar School, was elected Warden. He was succeeded in the following year by Professor W. Hearn.
In its early years the Senate served as the major forum for various groups within and around the university, most notably the professors, jostling for influence over policy and the administration of the University. In the record of its debates, especially in the 1880s, can be found a barometer of the intense educational debates that gripped the Victorian community at the time.