Kosterlitz was educated at the universities of Heidelberg, Freiburg, and Berlin where he obtained his MD in 1929. He remained there as an assistant until 1933 when, with the rise of the Nazis, he sought safety in Britain. He joined the staff of Aberdeen University in 1934 where he later served as professor of pharmacology and chemistry from 1968 until 1973 when he became director of the university's drug addiction research unit.

For many years Kosterlitz had been working on the effects of morphine on mammalian physiology when in 1975, in collaboration with J. Hughes, he made his most dramatic discovery. They were investigating the effect of morphine in inhibiting electrically induced contractions in the guinea-pig intestine and, to their surprise, discovered that the same effect could be produced by extracts of brain tissue. When it turned out that the effect of the extract could be inhibited by naloxone, a morphia antagonist, it seemed likely to them that they had in fact stumbled on the endogenous opiates, discussed earlier by Solomon Snyder, and named by them enkephalins.

They quickly succeeded in isolating two such enkephalins from pigs' brains and found them to be almost identical peptides consisting of five amino acids differing at one site only and consequently known as methionine and leucine enkephalins. When it was further shown that they possessed analgesic properties hopes were raised once more of the possibility of developing a nonaddictive yet powerful pain killer.