Heinrich XX was born at Offenbach, Landgraviate of Hesse-Darmstadt, younger surviving son of Heinrich XIII, Prince Reuss of Greiz (1747–1817), (son of Heinrich XI, Prince Reuss of Greiz and Countess Conradine Reuss of Köstritz) and his wife,Princess Wilhelmine Louise of Nassau-Weilburg (1765–1837), (daughter of Charles Christian, Prince of Nassau-Weilburg and Princess Carolina of Orange-Nassau).

At the death of his elder brother on 31 October 1836, Heinrich XX succeeded as the Prince Reuss of Greiz because of the Salic law that applied in the German principalities, his brother had died with no male heir.

The Prince, however, distinguished himself in military service in favor of the Austrian Empire.

Heinrich XX married on 25 November 1834 at Castle Haid in Haid to Princess Sophie of Löwenstein-Wertheim-Rosenberg (1809–1838), third daughter of Karl, Prince of Löwenstein-Wertheim-Rosenberg, and his wife, Countess Sophie Luise of Windisch-Graetz .

He married secondly on 1 October 1839 in Homburg vor der Höhe to Princess Caroline Amalie of Hesse-Homburg, eldest daughter of Gustav, Landgrave of Hesse-Homburg, and his wife, Princess Louise of Anhalt-Dessau.