Hänsch received his secondary education at Helmholtz-Gymnasium Heidelberg and gained his Diplom and doctoral degree from Ruprecht-Karls-Universität Heidelberg in the 1960s. Subsequently, he was a NATO postdoctoral fellow at Stanford University with Arthur L. Schawlow from 1970 to 1972. Hänsch became an assistant professor at Stanford University, California from 1975 to 1986. He was awarded the Comstock Prize in Physics from the National Academy of Sciences in 1983. In 1986, he received the Albert A. Michelson Medal from the Franklin Institute. In the same year Hänsch returned to Germany to head the Max-Planck-Institut für Quantenoptik. In 1989, he received the Gottfried Wilhelm Leibniz Prize of the Deutsche Forschungsgemeinschaft, which is the highest honour awarded in German research. In 2005, he also received the Otto Hahn Award of the City of Frankfurt am Main, the Society of German Chemists and the German Physical Society.  In that same year, the Optical Society of America awarded him the Frederic Ives Medal and the status of honorary member in 2008.
One of his students, Carl E. Wieman, received the Nobel Prize in Physics in 2001.
In 1970 he invented a new type of laser that generated light pulses with an extremely high spectral resolution (i.e. all the photons emitted from the laser had nearly the same energy, to a precision of 1 part in a million). Using this device he succeeded to measure the transition frequency of the Balmer line of atomic hydrogen with a much higher precision than before. During the late 1990s, he and his coworkers developed a new method to measure the frequency of laser light to an even higher precision, using a device called the optical frequency comb generator. This invention was then used to measure the Lyman line of atomic hydrogen to an extraordinary precision of 1 part in a hundred trillion. At such a high precision, it became possible to search for possible changes in the fundamental physical constants of the universe over time. For these achievements he became co-recipient of the Nobel Prize in Physics for 2005.