He was educated at Rugby School, Warwickshire then moved to Madras, India and became a writer in the Madras Civil Service from 19 May 1824.
He was the elder brother of Arthur Conolly, the famous British Captain of the Indian Army and explorer of Central Asia. He later served in Bellary in central India. While District Collector and Magistrate of Malabar Conolly was known for his Conolly Canal, initiated 1848, and Conolly Teak Plot.
The teak plantation was a pioneering example of systematic forest management.
lieutenant contained some of the finest pieces of the tropical hardwood teak. The plantations were constructed by the Madras Government for the supply of teak timber to the port of Bombay.
He is also remembered for his planning a coastal waterway in Malabar — what is known today as the Conolly Canal (although the introduction of railways around the time the canal was being completed had eclipsed its importance). On the evening of 11 September 1855, at around nine o"clock Conolly was attacked at the Collector"s Residence at West Hill Bungalow, Calicut by a small group of Mappilas.
The murderers, Valassery Emalu, Puliyankunnath Thenu (who had escaped from prison at Calicut a month before) and Haiderman, a hairdresser, were eventually tracked and shot dead by the government forces led by Major Haly and Captain Davis (in an encounter after 6 days at large at Edavannappara in Thiruvambadi).
The Mappila rebels were using these escaped prisoners to murder Henry Conolly who suggested the idea of exile of religious leader Sayid Fasal Pukkoya Tangal of Mambrum.