Tiselius was born in Stockholm, Sweden, and educated at the University of Uppsala, where he became the assistant of Theodor Svedberg in 1925. He obtained his PhD in 1930 and his whole career was spent at Uppsala where, in 1938, a special research chair in biochemistry was created for him, which he occupied until 1968.

Tiselius's doctoral thesis was on electrophoresis – a method of separating chemically similar charged colloids. An electrical field is applied to the sample, and particles with different sizes migrate at different rates to the pole of opposite charge, enabling them to be detected and identified. The method was not initially very successful but by 1937 Tiselius had made a number of improvements to the apparatus. Using the technique on blood serum Tiselius confirmed the existence of four different groups of proteins – albumins and alpha, beta, and gamma globulins. Tiselius also conducted work on other methods for the separation of proteins and other complex substances in biochemistry including chromatography (from 1940) and partition and gel filtration (from the late 1950s).

In 1948 he was awarded the Nobel Prize for chemistry for his work on electrophoresis and other new methods of separating and detecting colloids and serum proteins. After the war Tiselius played an important role in the development and organization of science in Sweden, serving (1946–50) as chairman of the Swedish Natural Science Research Council.