On the death of his father on 28 June 1800, Heinrich succeeded him as Prince Reuss of Greiz.

After the devastation of Greiz by a fire in 1802, Heinrich XIII ordered that the city be rebuilt in a neoclassical style, and he moved his residence from the Oberes Schloss (Upper Castle) to the Unteres Schloss (Lower Castle), to be more in contact with the people and social life of the Principality.

Heinrich XIII distinguished himself in his military service to Austria as a field marshal, to the point of being considered one of the Emperor Joseph II's best friends.

At the Congress of Vienna he was involved in a territorial dispute with the Kingdom of Saxony, from which he emerged victorious and won the domain of the cities of Altgommla and Kühdorf.

Heinrich XIII was married on 9 January 1786 in Kirchheimbolanden to Princess Wilhelmine Louise of Nassau-Weilburg (1765–1837), fourth child and second daughter of Charles Christian, Prince of Nassau-Weilburg, and his wife, Princess Carolina of Orange-Nassau.