Gustav Kirchhoff was born in Königsberg, East Prussia, the son of Friedrich Kirchhoff, a lawyer, and Johanna Henriette Wittke. He graduated from the Albertus University of Königsberg in 1847 where he attended the mathematico-physical seminar directed by Franz Ernst Neumann and Friedrich Julius Richelot. He married Clara Richelot, the daughter of his mathematics professor Richelot. In the same year, they moved to Berlin, where he stayed until he received a professorship at Breslau.

Kirchhoff formulated his circuit laws, which are now ubiquitous in electrical engineering, in 1845, while still a student. He completed this study as a seminar exercise; it later became his doctoral dissertation. He proposed his law of thermal radiation in 1859, and gave a proof in 1861. He was called to the University of Heidelberg in 1854, where he collaborated in spectroscopic work with Robert Bunsen. Together Kirchhoff and Bunsen discovered caesium and rubidium in 1861. At Heidelberg he ran a mathematico-physical seminar, modelled on Neumann's, with the mathematician Leo Koenigsberger. Among those who attended this seminar were Arthur Schuster and Sofia Kovalevskaya. In 1875 Kirchhoff accepted the first chair specifically dedicated to theoretical physics at Berlin.

In 1862 he was awarded the Rumford Medal for his researches on the fixed lines of the solar spectrum, and on the inversion of the bright lines in the spectra of artificial light.

He contributed greatly to the field of spectroscopy by formalizing three laws that describe the spectral composition of light emitted by incandescent objects, building substantially on the discoveries of David Alter and Anders Jonas Angstrom (see also: spectrum analysis)

Kirchhoff died in 1887, and was buried in the St Matthäus Kirchhof Cemetery in Schöneberg, Berlin.