Alexis was born in Burgsteinfurt, Kingdom of Prussia on 17 November 1845 and was the fourth child and eldest son of Ludwig Wilhelm, Prince of Bentheim and Steinfurt (1812–1890) and his wife Landgravine Bertha of Hesse-Philippsthal-Barchfeld (1818–1888).

Alexis was a brother of Adelheid, Landgravine Wilhelm of Hesse-Philippsthal-Barchfeld (1840–1880), Juliane, Landgravine Wilhelm of Hesse-Philippsthal-Barchfeld (1842–1878), Marie, Princess of Sayn-Wittgenstein-Hohenstein (1843–1931), Prince Karl of Bentheim and Steinfurt (1848–1854), and Prince Georg of Bentheim and Steinfurt (1851–1939).

In 1873, he advanced to first lieutenant and then to Rittmeister in the Regiment der Gardes du Corps in 1875.

In 1902, he was awarded the uniform of the Regiment der Garde du Corps Lieutenant General.

Alexis succeeded his father Ludwig Wilhelm to the headship of the Princely House of Bentheim and Steinfurt.