Irek Mukhamedov was trained at the Ballet Academy of the Bolshoi Theatre in Moscow (1970 – 1978). His exceptional ballet career started in 1978, when he became a First Soloist with the Moscow Classical Ballet Company. From 1981 to 1990, he was a Principal Dancer at the Bolshoi Ballet and then pursued his artistic career in London, where he was a Senior Principal Dancer at the Royal Ballet until 1998 and from 1998 to 2004, a Guest Principal Dancer of the same ballet ensemble.  In that period of time, he also performed as a Principal Dancer with the Paris Opera Ballet, Royal Ballet of Flanders, State Opera Ballet in Vienna, Helsinki Ballet, La Scala Theatre Ballet in Milan, Scottish Ballet, Ballet Ensemble of the Opera National de Bordeaux, English National Ballet, Birmingham Royal Ballet as well as in the ballet ensembles in Santiago, Wiesbaden, Warsaw and the Australian National Ballet.

He danced all the leading mail roles in the classical repertoire, i.e. the choreographies, created by Yuri Grigorovich, Kenneth MacMillan, Frederick Ashton, George Balanchine, Massine (Leonid and Lorca), Roland Petit, Twyla Tharp, Rudolf Nureyev, David Bintley, Ashley Page and William Tuckett. He also danced quite a number of roles in the modern ballet pieces by Kim Brandstrup and Darshan Singh Buller. Irek Mukhamedov has also established himself as a very successful choreographer.  

He has already staged the following choreographies: Swan Lake for the Warsaw National Ballet (2001) , The Four Horsemen and The Swords Dance for a Gala Charity Evening at the London Coliseum (2001), Solo Piece for the Nureyev Gala Evening in Bordeaux (2002), Beautiful Evening (Bonne Soirée) for the Arts Educational School Tring (2002), The King and the Beggar for the London Children's Ballet (2003), Solo Piece and a special choreography for the students at the Royal Ballet School to mark the solemn announcement of the Benois de la Dance (2003), Spanish Capriccio for the English National Ballet (2004), Montevideo Café Concert, created for the tour in Norway (2004), Spartacus for the Hong Kong Ballet (2005), A Midsummer Night's Dream for the Elmhurst Dance School (2006), Don Quixote Suite for the London Dance Studio (2007), Giselle, Evgeny Onegin and Aida for the Greek National Opera and Ballet (in 2008 and 2009).

He has been sharing his exceptional experience as a Ballet Master and Pedagogue with different ballet schools and ensembles (Royal Ballet in London, English National Ballet, Bordeaux Ballet, Scottish Ballet and Birmingham Royal Ballet). He is a Principal Guest Teacher at the English National Ballet School, and he teaches at the Elmhurst Dance School (in collaboration with the Birmingham Royal Ballet) as well as at the Ankara and Istanbul Ballet Companies in Turkey.

Before he took over his post at the Slovenian National Theatre Opera and Ballet Ljubljana, he was an Artistic Director of the Ballet Ensemble of the Greek National Opera and Ballet. Among other things, Irek Mukhamedov is also a President of the Legat Foundation and Vice President of the Arts Educational School Tring. He received a number of prestigious awards and recognitions: Grand Prix of the International Ballet Competition in Moscow (1981), Title of the Meritorious Artist of the Russian Republic (1985), Hans Christian Andersen Award for the Best Dancer in the World (1988), Dancer of the Year Title presented by the Dance and Dancers Magazine (1992), Dancer of the Year Title presented by the Independent on Sunday (1992), Dance Award, presented by the Evening Standard (1992), Gino Tani Award (Italy, 1992), Benois de la Danse Award (Paris, 1996), Nizhinsky Medal (1998) and Order of the British Empire (2000).