Dobbs was educated at Winchester College and Brasenose College, Oxford. He joined the Indian Civil Service in 1892, and in 1903 he was sent to repair boundary pillars erected by the Afghan Boundary Commission along the Russo-Afghan border. After several other posts, he served as the Chief Commissioner of Balochistan 1917–1919. Dobbs was the British Representative on the Kabul Mission in January 1921, during which he met with Afghan Foreign Minister Mahmud Tarzi to discuss Anglo-Afghan friendship.
The result was the Anglo-Afghan Treaty of 22 November 1921, which confirmed the Indo-Afghan border, established diplomatic ties between London and Kabul, and defined special trade agreements. He later served as High Commissioner to the Kingdom of Iraq from 1923 to 1929, the longest time this position was held by anyone during the course of the Iraq Mandate.
He was appointed a Companion of the Order of the Indian Empire (CIE) on 31 May 1905 for his services in Afghanistan, and appointed a Companion of the Order of the Star of India (CSI) on 18 August 1916 for meritorious war services. In January 1921, he was knighted as a Knight Commander of the Order of the Indian Empire (KCIE),
He was appointed a Knight Commander of the Order of the Star of India in 1923, a Knight Commander of the Order of St. Michael and St. George (KCMG) in the 1925 Birthday Honours List and a Knight Grand Cross of the Order of the British Empire (GBE) on 1 March 1929.
- A monograph on the pottery and glass industries of the North-Western Provinces and Oudh, North-Western Provinces and Oudh Government Press, Allahabad, 1895
- Korah (A drama, in verse), Grant Richards, London, 1903
| Chief Commissioner of Balochistan
5 December 1917 – 1 September 1919
Armine Brereton Dew
Sir Percy Cox
| High Commissioner for Iraq and Commander-in-Chief therein
Sir Francis Humphrys
- Clements, Frank (2003). Conflict in Afghanistan: A Historical Encyclopedia. California. p. 73.
- Afghanistan Strategic Intelligence: British Records 1919-1970, Archive Editions Limited, 2002, p. 159-184
- Provinces of British India, rulers.org; accessed 21 March 2016.
- London Gazette, 6 June 1905
- London Gazette, 18 August 1916
- London Gazette, 1 January 1921
- London Gazette, 3 June 1925
- London Gazette, 1 March 1929