In 1984 Popovich joined the Russian Academy of Sciences' newly created All-Union Investigation Committee for Anomalous Aerial Phenomena and became head of the Academy's UFO Commission.

In the 2002 SciFi Channel documentary Out of the Blue, Popovich relays a sighting of a UFO next to the airplane he was travelling aboard as he was returning home from Washington D.C. with a delegation of scientists. The UFO was seen by everyone on board the plane. It was perfect triangle shaped and emitted a very bright, white light at a distance of about 1.5 kilometres (0.93 mi) and an altitude about 1,000 metres (3,300 ft) above the airplane. The object had an estimated speed of 1,500 kilometres per hour (930 mph) travelling parallel to the airplane and passed and overtook the plane in about 30 to 40 seconds.

Popovich was the president of the UFO association of Russia.