Born in Løgstør, Jutland to a poor family of fishermen, Horrebow entered the University of Copenhagen in 1703.

He worked his way through grammar school and university by virtue of his technical knowledge: he repaired mechanical and musical instruments and cut seals.

He worked as a household tutor from 1707 to 1711 to a Danish baron, and entered the governmental bureaucracy as an excise writer in 1711.

After repeatedly petitioning King Frederick IV, Horrebow became professor of mathematics at the University of Copenhagen in 1714.

Horrebow was a member of a number of scientific societies, including the Académie des Sciences (from 1746).