Stefan was educated in his native Klagenfurt and at the University of Vienna. In 1863 he became professor of mathematics and physics at Vienna University and remained there for the rest of his life.

Stefan's wide-ranging work included investigations into electromagnetic induction, thermomagnetic effects, optical interference, thermal conductivity, diffusion, capillarity, and the kinetic theory of gases. However, he is best remembered for his work on heat radiation in 1879. After examining the heat losses from platinum wire he concluded that the rate of loss was proportional to the fourth power of the absolute temperature; i.e., rate of loss = σT ⁴. In 1884 one of his students, Ludwig Boltzmann, showed that this law was exact only for black bodies (ones that radiate all wavelengths) and could be deduced from theoretical principles. The law is now known as the Stefan–Boltzmann law; the constant of proportionality, σ, as Stefan's constant.

Stefan was a good experimental physicist and a well-liked teacher. During his lifetime he held various important positions, including Rector Magnificus of the University (1876) and secretary (1875) then vice-president (1885) of the Vienna Academy of Sciences.