His parents were Albert Tyas Harden and Eliza Macalister. He was educated at a Tettenhall College, Staffordshire, and entered Owens College, now the University of Manchester, in 1882, graduating in 1885.
In 1886 Harden was awarded the Dalton Scholarship in Chemistry and spent a year working with Otto Fischer at Erlangen. He returned to Manchester as lecturer and demonstrator, and remained there until 1897 when he was appointed Chemist to the newly founded British Institute of Preventive Medicine, which later became the Lister Institute. He earned the degree Doctor of Science (D.Sc.) from the Victoria University (which included Owens College) in June 1902. Five years later, in 1907 he was appointed Head of the Biochemical Department, a position which he held until his retirement in 1930 (though he continued his scientific work at the Institute after his retirement).
Harden was knighted in 1926, and received several honorary doctorates. A Fellow of the Royal Society, he received the Davy Medal in 1935.