The grandson of Eastern European Jewish immigrants, Braterman was born and raised in London. He received his Master of Arts and DPhil degrees from Balliol College, Oxford.  In 1985 he received a DSc degree.
After postdoctoral research at University College London (adviser Robert Williams), and University of California at Los Angeles (advisers Herbert D. Kaesz and Mostafa El-Sayed), he worked in the chemistry departments of the University of Glasgow, where he rose to the rank of reader, and the University of North Texas as professor and chair, and later as Regents Professor, with several periods as visiting investigator at Scripps Institution of Oceanography at the University of California San Diego, and Sandia National Laboratories.
Braterman's work has been supported by the Robert A. Welch Foundation, the National Science Foundation, and NASA’s exobiology and astrobiology programs, for which he also served as an adviser.
In 2007, he returned to Glasgow where he is now an Honorary Senior Research Fellow.