Miloš Milošević was born in Split to an ethnic Serb family. He enrolled in the swimming school of the swimming club "Mornar" in 1980, which lasted four years. At the age of 14, he started competing in youth swimming competitions of SFR Yugoslavia. He won a total of eight gold medals as a junior.
He later moved to Rijeka, to the swimming club "Primorje". As a person of Serb descent, during the Croatian War of Independence he had considerable difficulty trying to compete for Croatia. He missed the 1992 Summer Olympics in Barcelona, but his talent eventually secured him a place in the national swimming team.
At the European Short Course Swimming Championships 2002 he won the silver medal in 50 meter butterfly. He retired from professional swimming in 2004. His personal best in the 50 meter butterfly event was 23.30 (1998), and in the 100 meter butterfly event 52.24 (1998).
He currently trains the youth at his swimming club "Primorje" in Rijeka.