Born in Amsterdam, as the son of the poet, teacher and philologist Anthonie Oudemans Sr., he entered Leiden University when he was just 16 as a student of the noted astronomer Frederik Kaiser. He became a high school teacher in Leiden when he was just 19 (1846). The next six years he worked on his dissertation on the determination of the latitude of Leiden. Next he studied asteroids and variable stars, meanwhile hoping for an academic appointment.
He married Pauline Adriana Verdam (the daughter of a well-known mathematics professor) in 1856. In the same year he was appointed a professor at Utrecht University and became director of its observatory for the first time. However, his interest drew him towards geography. He traveled to the Dutch East Indies as head surveyor, and worked in that capacity for 18 years, publishing his works on the triangulation of the island of Java in six books.
In 1874 he observed the Venus transit from the island of Réunion, although in bad weather. In 1889 he published a star map.