Minchev is a graduate of the Bulgarian State Conservatoire in Prof. Marin Goleminov's composition class.
Between 1968 and 1970 he majored under Rodion Shchedrin in Moscow and for several months he studied simultaneously under Aram Khachaturian.
In 1972 he received a UNESCO music fellowship to further his education in the USA, Great Britain and France.
In 1989 Georgi Mintchev was honoured as Senatore Accademico and was awarded the Lorenzo Magnifico European Prize of the Accademia Internationale Medicea in Florence.
His works have been performed in Bulgaria, France, Germany, Italy, Switzerland, Russia, Poland, the Czech Republic, Slovakia, Cuba, Columbia, Australia, Greece, Belgium, Austria, San Marino, USA, the Netherlands, Spain, Japan, Great Britain and Finland.