Adams was born in Tungkillo, South Australia, elder son of Henry Adams Sr., and soon after moved with his parents to a farm in Mount Barker. His father found work at the Callington mine. At age 14 Henry left school to work at the same mine. At 18 years of age he began preaching at the Mount Barker Methodist Church circuit, but resisted suggestions that he make the Church his vocation. In 1870, when the mine became uneconomic, he left Callington for Moonta. In 1878 he left to work as a carpenter for coachbuilder John Crimp, in Grenfell Street, Adelaide. A year later he went to work for the builder Nicholas W. Trudgen, also of Grenfell Street. He next joined the Government Way and Works Department, and rose to the position of engineer. When the Department shifted to Glanville he was transferred as patternmaker. He was involved in the Union movement, and in 1893 left the job to contest the seat of Sturt on the House of Assembly for the Labor Party. He was beaten, but was elected president of the Trades and Labor council, then in 1894 won a seat on the Legislative Council, and retired in 1902, and taking up residence in Devonport Terrace, Wayville.[2]
He was associated with the Railways Service Association, and for many years was secretary. He was for 28 years a director of the Co-operative Building Society[3] and treasurer of the Adelaide Cooperative Society. He was a longtime member of the Pirie Street Methodist Church, on the Council of the School of Mines, and the Board of Elder Homes. He was a former Secretary of the Amalgamated Railways Association.[4] He was for twenty years a trustee of the Savings Bank of South Australia.[2]
Henry had a brother John Adams in Broken Hill, and three sisters: Mrs. Chapel of Moonta, Mrs. Dunstan of Mallala and a Miss Adams.
He was married with two sons Henry Gordon Adams and Victor E. Adams, and a daughter, Mrs. Lattimore; he died at 4 Audley Avenue, Prospect, the home of his son H. G. Adams, and was buried at West Terrace Cemetery.