The first Registrar, William Barlow, was appointed part-time in 1874 and his department was responsible for the overall administration of the University. This included finance, the library, examinations, staff, students, buildings, accommodation and equipment. In 1965 following a decision by Council to institute a tripartite system of senior administration, the Registrar's Department was replaced by the Registrar's Office.

When South Australia was founded, the Governor determined matters of policy, made laws and was responsible to the United Kingdom Government for the management of the Colony. By the time of the establishment of University of Adelaide, policy matters were left to elected Members of Parliament. The Governor at this time was Right Honourable Sir James Fergusson, Bt (1869-1873). He was a strong supporter of the University and accepted membership of the University Association in November 1872. Successor Governors included:
Sir Anthony Musgrave, KCMG (1873-1877)
Lieutenant General Sir William F.D. Jervois, GCMG, CB (1877-1883)
Sir William C.F. Robinson, GCMG (1883-1889)
Right Honourable the Earl of Kintore, PC, GCMG (1889-1895)
Sir Thomas F. Buxton, Bt, GCMG (1895-1899)
Right Honourable Hallam, Lord Tennyson, KCMG (1899-1902)
Sir George R. Le Hunte, KCMG (1903-1909)
Admiral Sir Day Hort Bosanquet, GCVO, KCB (1909-1914)
Lieutenant Colonel Sir Henry L. Galway, KCMG, DSO (1914-1920)
Lieutenant Colonel Sir W.E.G. Archibald Weigall KCMG (1920-1922)
Lieutenant Colonel Sir G. Tom M. Bridges KCB, KCMG, DSO (1922-1927)

The University Association formed at its first meeting of "gentlemen favourable to the establishment of a university in Adelaide" in the classroom of Union College on 17 September 1872. The meeting was attended by:
The Lord Bishop of Adelaide (Chair)
The Ven. Archdeacon Marryat
The Very Rev. Dean Russell
Reverend Canon Farr
Reverend J. Jefferis
Reverend J. Davidson
Reverend H. Read
Reverend W.P. Wells
Reverend J. Henderson
Reverend J.C. Woods
Reverend W.W. Ewbank
Reverend A.T. Boas
Dr. Whittell
Mr. J.A. Hartley
Mr. J. Howard Clark
Mr. T. Magarey
Mr. A. Hay
Mr. D. Fowler
Mr. G. Young
The meeting was told that the unexpected success of Union College had led to a widespread conviction that sufficient grounds existed for attempting something of a more comprehensive and national character and the Association's aims were determined to secure further members and financial support, appoint professors and lecturers, arrange classes and to establish a university formally by Act of Parliament.
After successfully achieving its aims, the Association was dissolved on 7 May 1875 and all of its books, papers and other property were transferred to the University of Adelaide.

The Right Reverend Augustus Short, DD, Lord Bishop of Adelaide played an important supporting role in the establishment of the University of Adelaide. He chaired the initial and subsequent meetings of the University Association and was elected as the first Vice-Chancellor in 1874 and Chancellor from 1876-1883.

On 28 February 1872 a meeting of representatives of the Baptist, Congregational and Presbyterian churches decided to found a college to provide young men with an education beyond school level to train those desiring to devote themselves to the work of the Christian ministry. Classes commenced a few months later and were an immediate success. Demand soon outgrew supply of instruction and money and a suggestion was made to Walter Watson Hughes that he might wish to donate to the College. His resulting promise of £20,000 initiated the movement to form a university in Adelaide which subsequently replaced the College in 1874.

The first local government in Australia was formed on 31 October 1840 with the election of a Mayor, three Aldermen and fifteen Councillors to the new Adelaide Corporation. This followed a petition from the residents (totalling around 2000) for the "rights and privileges" of their own Council. The first Mayor was James Hurtle Fisher and the first Council meeting was held on 4 November 1840.