He was the second son of Frederick Cornelis Engelbrecht (1804–1869), the main administrator of the Royal Netherlands Navy in the Dutch Indies (present Indonesia).

Engelbrecht was one of the intellectual architects of the Dutch Ethical Policy, which eventually led to the independency of Indonesia.

After completing his studies, Engelbrecht moved back to the Dutch East Indies to become a civil servant in the colonial administration.

In this function he worked actively on the formation of the Dutch Indies as a state within the colonial empire of the Netherlands.

In 1891, Governor-General Cornelis Pijnacker Hordijk assigned Engelbrecht with drafting a Governmental regulation on this issue.

In 1893 Engelbrecht became a member of the so-called Raad van Nederlandsch-Indië (Council of the Dutch East Indies), the de facto government of the colony.

The couple had one son, Johannes Frederik Engelbrecht (1863–1911), who became a member of Supreme Court of the Dutch Indies.