Henry Allen Atkins was born in Waterbury, Vermont, on September 18, 1827. His mother, a member of the Barr family, was born in Lowell, Massachusetts. Atkins' other ancestors include the Allen family of Ticonderoga fame. As a young child, Atkins went to live with his uncle in Ohio following his parents' deaths. After his graduation from Ohio's Twinsburg Instituite, he worked in Ohio until 1849, when he travelled to California to mine for gold. He spent nine years mining in California before travelling to British Columbia and Seattle, where he spent the remainder of his life. Atkins worked at a number of jobs in Seattle, including as a pile driver and as a clerk at Dexter Horten, which later became known as Atkins & Shoudy. In 1869, Atkins was appointed as the first mayor of Seattle. He also served as the King County Sheriff (1873), Regent of the Territorial University (1874-1878), and Master of the St. John's Lodge of Masons.

In 1867, Atkins married Mary J. Osborne, who had travelled with her son, Eben S.Osborne, to Seattle from Massachusetts on the Mercer expedition the previous year. Before her marriage to Atkins, she taught school for a short period at Chambers Prairie, near Olympia. Together, Henry and Mary had three children, Mary Emma, Persis Amelia, and Frank Rufus.

Atkins died on June 24, 1885 as the result of complications following a severe blow to the head sustained while splitting a pile in Victoria two years earlier.