Bessel was born into a poor family in Minden, Germany, and started work as a clerk. His interest in and aptitude for astronomy brought him to the attention of Heinrich Olbers, who obtained a position for him in the observatory at Lilienthal. Four years later he was entrusted with the construction of the observatory at Königsberg and appointed its director.

Bessel made many advances in astronomy. He cataloged the position of 50,000 stars down to the ninth magnitude between 15°S and 45°N and, using James Bradley's results, achieved new levels of accuracy. He also made careful observations of 61 Cygni and was able to detect a parallax of 30 arc seconds and to calculate the star's distance – the first such determination – as 10.3 light years. (The distance is now known to be 11.2 light years.) Although Bessel was the first to announce the detection of parallax (1838), Thomas Henderson had in fact measured it in 1832 in his observations of Alpha Centauri.

Bessel's other great discovery came after observing a slight displacement in the proper motion of Sirius, which he explained as the effect of an orbit around an unseen star, and announced in 1844 that Sirius was a double star system having a dark companion. Sirius B was detected optically by Alvan Clark in 1862. Bessel made a similar claim for Procyon whose companion was discovered optically in 1895. He also noted irregularities in the motion of Uranus and suggested that they were caused by an unknown planet, but died just before the discovery of Neptune.

In mathematics Bessel worked on the theory of the functions, named for him, that he introduced to determine motions of bodies under mutual gravitation and planetary perturbations. They still have a wide application in modern physics.