Neher was born in Landsberg am Lech, Upper Bavaria, the son of Elisabeth (née Pfeiffer), a Teacher, and Franz Xaver Neher, an executive at a dairy company. He studied physics at the Technical University of Munich from 1963 to 1966.
In 1966, he was awarded a Fulbright Scholarship to study in the US. He spent a year at the University of Wisconsin–Madison, and earned a master's degree in biophysics. While at the Charles Stevens Laboratory at Yale University for post-doctoral work he met fellow scientist Eva-Maria Neher, whom he married in 1978 and subsequently the couple had five children – Richard, Benjamin, Carola, Sigmund, and Margret.
In 1986, he was awarded the Louisa Gross Horwitz Prize from Columbia University together with Bert Sakmann. In 1987, he received the Gottfried Wilhelm Leibniz Prize of the Deutsche Forschungsgemeinschaft, which is the highest honour awarded in German research. Along with Bert Sakmann, he was awarded the Nobel Prize in Physiology or Medicine in 1991 for "their discoveries concerning the function of single ion channels in cells". Neher and Sakmann were the first to record the currents of single ion channels on a live cell (they were first recorded using the lipid bilayer method) through their development of the patch-clamp technique, a project Neher began as a postdoctoral research associate in the laboratory of Charles F. Stevens at Yale.
Neher was awarded an Honorary degree from the University of Pavia in 2000. He was elected a Foreign Member of the Royal Society (ForMemRS) in 1994.
In 2003 Neher was one of 22 Nobel Laureates who signed the Humanist Manifesto.