Born in Berlin, Germany, Wittig was educated at the university of Marburg. He worked at Braunschweig (1932–37), at Freiburg im Breisgau (1937–44), and at Tubingen (1944–65). In 1965 he became director of the Chemical Institute at Heidelberg, a post he held until his retirement in 1967.

Wittig worked extensively in organic chemistry, in particular on the chemistry of carbanions – negatively charged organic ions such as C₆H₅ ^–. In this work he discovered a class of reactive phosphorus compounds of the type (C₆H₅)₃P:CH₂. Such compounds (known as ylides) are able to replace the oxygen of a carbonyl group C=O by a CH₂ group, to give C=CH₂. This reaction, known as the Wittig reaction, is of immense importance in the synthesis of certain natural compounds, such as prostaglandin and vitamins A and D₂. Wittig also discovered a useful directed form of the aldol condensation. He was awarded the Nobel Prize for chemistry in 1979.