Born on the Caribbean island of Sint Eustatius (also known as Statia), part of the islands of the Dutch Antilles, Jacob Marcus settled with his father in Amsterdam in 1783, at the age of nine. When his father died a year later, Marcus was brought up by a guardian, the merchant Balthazar Ortt. He received training in drawing from the artist Steven Goblé and in engraving from the well-known printmaker and draughtsman Reinier Vinkeles – one of the few pupils Vinkeles accepted - while also studying at the Stadtstekenacademie in Amsterdam, where he won a gold medal in 1798.

Active primarily as a draughtsman and printmaker, Marcus produced landscapes, genre scenes and portraits, as well as reproductive etchings, engravings and lithographs after the work of such earlier artists as Jacob Cats and Jan Steen, among others. A member of the Koninklijke Academie in Amsterdam, Marcus was also a founder member of the Amsterdam Art Society (the Amsterdams Kunstgenootschap) in 1801. Between 1807 and 1816 he published a series of 106 prints under the title Studiebeelden en Fragmenten, and in 1820 was appointed a professor and director of the Akademie van Beeldende Kunsten in Amsterdam. The artist died six years later, at the age of fifty-two.