Todd graduated from the university in his native city of Glasgow in 1928 and spent a further year there on a Carnegie Scholarship before going to the University of Frankfurt, Germany. He received doctorates from both Frankfurt (1931) and Oxford (1933) universities and in 1934 joined the medical faculty at Edinburgh University where he began work on thiamine (vitamin B₁). He continued this research at the Lister Institute of Preventive Medicine, London, and worked out the structure and synthesis of thiamine.

In 1938 Todd became professor of chemistry at Manchester University and continued vitamin studies on vitamins E and B_{1 2}. He also isolated the active principle from Cannabis, extracting the compound cannabinol from cannabis resin.

Todd transferred to Cambridge in 1944 to become professor of organic chemistry, a post he held until his retirement in 1971. At Cambridge he synthesized all the purine and pyrimidine bases that occur in nucleic acids (DNA and RNA) and found their structures. This was an important development in the understanding of the structure of the hereditary material and verified the formulae that Phoebus Levene had suggested for the nucleotide bases. Todd also synthesized various coenzymes related to these compounds, e.g., flavin adenine dinucleotide (FAD), and synthesized the energy-rich compounds adenosine diphosphate and triphosphate (ADP and ATP) so important in energy transfer in living cells.

The 1957 Nobel Prize for chemistry was awarded to Todd for these contributions to biochemistry and the understanding of the gene. Todd was knighted in 1954, raised to the British peerage as Baron Todd of Trumpington in 1962, and from 1975 to 1980 was president of the Royal Society. He also published an account of his busy life in his autobiography A Time to Remember (1983).