His father was Jan Apostool, a Mennonite and a merchant in animal skins and cocoa beans, and his mother was Cornelia de Witte.

From 1784 to 1786, he was a pupil of landscape painter Hendrik Meijer at the art academy back in Amsterdam.

[2] In 1802, Apostool returned to his position as Commissary-general of Commerce in London, and he negotiated the release of Batavian ships.

[2] In 1808, Apostool was appointed director of the Royal Museum in Amsterdam, which office he held until his death.

[2] He engraved a portrait of Lavinia Fenton, afterwards Duchess of Bolton, after Hogarth, as well as landscapes for the Beauties of the Dutch School, Select Views in the South of France, Travels through the Maritime Alps, and Daniell's Views of Hindostan.