Popov, the son of a priest from Bogoslavsky in Russia, was educated in a seminary to prepare him for a clerical profession. His interest however turned to physics and mathematics, which he studied at the University of St. Petersburg between 1877 and 1882. While still a student he worked in 1881 at the Electrotekhinik artel, which operated Russia's first electric power stations. He taught for a short time at the university and then in 1883 joined the staff of the Torpedo School at Kronstadt, where naval specialists were trained in all branches of electrical engineering and where he was able to conduct his own research. He subsequently became head of the physics department and remained there until 1900. Popov returned to St. Petersburg as professor at the Institute of Electrical Engineering in 1901 and was appointed its director in 1905. Later that year Popov's health was undermined by his refusal to take severe action against the political disturbances among his students and he died shortly after.

In 1888 Heinrich Hertz had produced and transmitted electromagnetic waves, arousing the interest of many scientists. Popov began experiments on the transmission and reception of the so-called Hertzian waves (radio waves) somewhat earlier than Marconi. He modified the coherer developed by Oliver Lodge for detecting these waves, making the first continuously operating detector. Connecting his coherer to a wire antenna, he was able in 1895 to receive and detect the waves produced by an oscillator circuit. His interests at this time, however, seemed more toward the investigation of atmospheric phenomena such as thunderstorms and lightning; he used his coherer connected to lightning conductors for this purpose. Stimulated by the 1896 patent awarded to Marconi, Popov again turned his attention to radio transmission and enlisted the help of the Russian navy. In 1897 he was able to transmit from ship to shore over a distance of 3 miles (5 km) and managed to persuade the naval authorities to begin installing radio equipment in its vessels. By the end of 1899 he had increased the distance of his ship to shore transmissions to 30 miles (48 km). He received little encouragement or support from the Russian government and did not commercialize his discoveries.

The Russian claim that Popov invented radio communication is not widely accepted, although he did publish in January 1896 a description of his receiving apparatus that coincides very closely with that described in Marconi's patent claim of June 1896. Popov is credited however with being the first to use an antenna in the transmission and reception of radio waves.