Rashidov was born in Dimitrovgrad to ethnic Turkish parents; however, he moved to Haskovo with his parents at age two. His mother Kadrie Lyatifova, a singer of Bulgarian and Turkish folk songs, died in a car crash when he was in primary school. His father Lyatif Rashidov was a miner in Madan and so was his brother Ruzhdi who died at 36 of cancer. Until seventh grade, Rashidov lived and studied at an orphanage in Studen Kladenets near Kardzhali. Rashidov then studied mining electrics and mechanics in Madan. He graduated from the National Academy of Arts in Sofia in 1978. As a sculptor, Rashidov has authored statuettes for a number of prominent prizes, as well as many large-scale works.
Despite being an ethnic Turk, Rashidov as a prominent social figure has been an outspoken critic of the Movement for Rights and Freedoms. He participated in the 2009 Bulgarian parliamentary election as GERB's voting list leader and proportional candidate in Kardzhali Province and became the first non-Movement for Rights and Freedoms candidate in many years to be elected to parliament from that constituency. When GERB won the election and formed a government in 2009, Rashidov was the party's Minister of Culture.
In 2014, when GERB formed a coalition government, Rashidov was for the second time the party's Minister of Culture. He is currently holding this position.
Rashidov is married and has a child. In 2001, he was briefly arrested for assaulting a policeman.