The Department of External Affairs [I] was established on 1 January 1901 (Commonwealth of Australia Gazette No. 1 of 1 January 1901, p. 4) and was one of the first seven Departments of State to be established when Australia was constituted a Commonwealth. The functions of the Department as outlined in the first administrative arrangements order were: 

 Fisheries - extra-territorial
 Naturalization and aliens
 Immigration and emigration
 Influx of criminals
 External affairs
 Pacific Islands
 High Commissioner
 Communications with States
 Governor-General and Executive Council offices
 Officers of Parliament

The Acts administered by the Minister for External Affairs [I] were:

 Pacific Island Labourers Act 1901 
 Immigration Restriction Act 1901
 Royal Commissions Act 1902
 Naturalization Act 1903
 Extradition Act 1903
 Papua Act 1905
 Contract Immigrants Act 1905
 Immigration Restriction Amendment Act 1905
 High Commissioner Act 1909
 Northern Territory Acceptance Act 1910
 Northern Territory (Administration) Act 1910
 Norfolk Island Act 1913

The function of personnel administration, later exercised by the Public Service Commissioner's Branch and its successor, the Public Service Board under the Prime Minister's Department, passed from the Department of External Affairs [I] to the Department of Home Affairs [I] (CA 8) in 1902.
 
From 1901 to 1904 the Minister for External Affairs was also Prime Minister, but in 1904 a separate Prime Minister's office (CA 588) was established. This Office remained a part of the Department of External Affairs [I] until the creation of the Prime Minister's Department (CA 12) in 1911. Functions of the Department which passed to the Prime Minister's Department in that year included:  
 
 communication or liaison with the States, the Governor-General, the
 Federal Executive Council (the Official Secretary to the
 Governor-General and Secretary to the Executive Council, and his  
 staff, being officers of the Department);
 relations with Parliament and its officers;
 the issue of Royal Commissions; and
 the publication of the 'Commonwealth of Australia Gazette'.
 
On the abolition of the Department on 14 November 1916 the Prime Minister's Department took over responsibility for external affairs, consular appointments and the issue of passports, the High
Commissioner in Great Britain and relations with Pacific islands, the Department of Home and Territories (CA 15) assumed the functions of immigration, naturalization, policy and laws affecting aliens and people of other races (except aborigines), extra-territorial fisheries, and responsibility for the Northern Territory (previously administered through the Northern Territory Branch under a lands Officer, later a Draughtsman) and the Attorney-General's Department (CA 5) assumed responsibility for extradition.
 
The following were Ministers for the Department of External 
Affairs [I]:
 
 1 Jan 1901 - 24 Sep 1903  : Edmun Barton 
24 Sep 1903 - 27 Apr 1904  : Alfred Deakin 
27 Apr 1904 - 17 Aug 1904  : William Morris Hughes
18 Aug 1904 -  5 Jul 1905  : George Houstoun Reid
 5 Jul 1905 - 13 Nov 1908  : Alfred Deakin 
13 Nov 1908 -  1 Jun 1909  : Egerton Lee Batchelor 
 2 Jun 1909 - 29 Apr 1910  : Littleton Ernest Groom 
29 Apr 1910 -  8 Oct 1911  : Egerton Lee Batchelor 
14 Oct 1911 - 24 Jun 1913  : Josiah Thomas 
24 Jun 1913 - 17 Sep 1914  : Patrick McMahon Glynn 
17 Sep 1914 -  9 Dec 1914  : John Andrew Arthur 
14 Dec 1914 - 14 Nov 1916  : Hugh Mahon 


References:

(1) C A Hughes and B D Graham, Handbook of Australian Government and
    Politics, 1890 - 1964, ANU Press 1968. 
(2) A A Hunt, CBE was Secretary to the Department from 1 May 1901 to
    13 November 1916.
 

Historical agency address
1901-1916: Melbourne, Victoria
Legislation administered
Creation: Federal Executive Council Minutes, No 1 of 1901 
Abolition: Federal Executive Council Minutes, No 8 of 1917 (PM No 134)

Unregistered links

1902: Queensland, Chief Secretary's Office (for Papua)
1904: All States, Chief Secretaries (for naturalization)
1914: New South Wales, Norfolk Island Office (for Norfolk Island)