The composer of the opera 'The Magic Flute' is Wolfgang Amadeus Mozart, a prolific and influential composer of the Classical period. Mozart was born in Salzburg, Austria in 1756 and composed over 600 works during his lifetime. He is widely regarded as one of the greatest composers of all time and his works are still performed today. Mozart's most famous opera, 'The Magic Flute', was first performed in Vienna in 1791.