Baels was born on 18 January 1878 in Ostend, Belgium. He was the son of Julius Ludovicus Baels (1851–1896), a shipowner, and Delphina Alexandrina Mauricx (1848–1931), who married in Ostend in January 1876.
Baels was married to Anne Marie de Visscher (1882–1950), a daughter of Adolphus Gustavus de Visscher and his wife, Alicia Victoria Carolina Opsomer. She was a descendant of Count Felix de Muelenaere, member of the Belgian National Congress (when founding the Kingdom of Belgium in 1831), who was a three-time Minister of Foreign Affairs between 1831 and 1841. Together, Anne Marie and Henri were the parents of eight children, including:
Lydia Baels (1920–1990), who married Jean-Jacques Cartier, a son of jeweler Jacques-Théodule Cartier and the former Nelly Harjes.[3]
Their other children included Elza Baels, Susanne Baels, Ludwina Baels, Walter Baels, Hermann Baels (who married), and Henry Baels. Baels died on 14 June 1951 in Knokke, Belgium.[2]
Through his daughter Lydia, he was a grandfather of two Viviane Mary Cartier (b. Dorking, 22 December 1946) and N. N. Cartier (b. Dorking, 26 April 1948).[3]