Born in Vernon, Connecticut, Henderson graduated from Beloit College (1867) and Union Theological Seminary (1870). He married Emma Jane Dickinson in 1871, was ordained to the Congregational ministry in 1872, and sailed for China under the American Board of Commissioners for Foreign Missions (ABCFM).
He did evangelistic work at Tientsin among the poor, believing that "Christianity always and everywhere begins with the lowest stratum of society and works upward," as he wrote in one of many articles in the Chinese Recorder. He contributed frequently to the Celestial Empire (Shanghai), China Mail (Hong Kong), International Review of Missions, Missionary Herald, Outlook (New York), and the North China Daily News and Herald, China's principal English language newspaper.
In 1890 Smith went to Pangzhuang, Shantung, where he did evangelistic work and began a series of books on Chinese life which helped make him a widely known interpreter of China. In 1900 he was caught at Peking in the Boxer Rebellion, described in his two-volume China in Convulsion (1901). While in the United States to assist an ABCFM fund-raising effort in 1906, he secured an interview with President Theodore Roosevelt and persuaded him that a substantial portion of Boxer indemnity funds should be used to create an American-style college in China; Ts'ing-hua (Qinghua) University was the result.
On his return Smith was made missionary-at-large, residing at Tongzhou. He was American chairman of the China Centenary Conference in 1907, a member of the China Continuation Committee, which coordinated most Protestant efforts, and a member of the editorial board of the Chinese Recorder. He also attended the World Missionary Conference at Edinburgh in 1910. In 1926 he retired at Claremont, California.