Genée was the son of the opera singer (bass) and manager of the Danziger Stadttheaters Friedrich Genée (1795-1856).
He studied first medicine, then music and took composition lessons with Adolf Stahlknecht (1813-1887) in Berlin. From 1848 he was active as a theatrical conductor in Reval, Riga, in 1852/1853 in Cologne, Dusseldorf, Aachen, Gdansk, in 1857 in Mainz, in 1864/65 in Prague, then in the court opera Schwerin as well as in the Deutschen Oper in Amsterdam.
Richard Genée was friends with Friedrich von Flotow and worked from 1868 and for a decade as a conductor at the Theater an der Wien. Together with Franz Zell (Operettenfirma Zell und Genée) he wrote a huge bunch of librettos for operettas de Millöcker, Suppé, Ziehre. Among others, the two best-known operettas whose texts he cowrote are Die Fledermaus of Johann Strauss (together with Karl Haffner) and Der Bettelstudent of Karl Millöcker (together with Franz Zell).
In 1876, he composed the operetta Der Seekadett. In Chess, there is an “opening trap” called Seekadett after this operetta.
Asides from composing and conducting, Genée also did translation work of Jacques Offenbach and Gilber & Sullivan pieces. He retired from conducting age 55 and lived comfortable enjoying his popularity until the age of 72. He spent the winter months in Berlin, the summer months in Vienna, Preßbaum or in his dwelling house in Baden – where he passed away “during a health resort stay” and was buried on 17 June, 1895 on the town cemetery. The funereal mourners included Johann Strauss, Karl Millöcker and Karl Komzák.