Braun, who was born in Fulda, Germany, studied at Marburg and, in 1872, received a doctorate from the University of Berlin. He taught in various university posts. In 1885 he became professor of experimental physics at Tübingen and in 1895 he became professor of physics at Strasbourg.

In 1874, Braun observed that certain semiconducting crystals could be used as rectifiers to convert alternating to direct currents. At the turn of the century, he used this fact in the invention of crystal diodes, which led to the crystal radio. He also adapted the cathode-ray tube so that the electron beam was deflected by a changing voltage, thus inventing the oscilloscope and providing the basic component of a television receiver. His fame comes mainly from his improvements to Marconi's wireless communication system and, in 1909, they shared the Nobel Prize for physics. Braun's system, which used magnetically coupled resonant circuits, was the main one used in all receivers and transmitters in the first half of the 20th century.

Braun went to America to testify in litigation about radio patents but, when the United States entered World War I in 1917, he was detained as an alien and died in New York a year later.