Dove was born in Liegnitz in the Kingdom of Prussia. Dove studied history, philosophy, and the natural sciences at the University of Breslau from 1821 until 1824. In 1824 he continued his education at the University of Berlin, finishing in 1826. In 1826, he became a Privatdozent and in 1828 a Professor extraordinarius at the University of Königsberg. In 1829, he moved to Berlin and taught at the Friedrich Wilhelm Gymnasium.
In 1845 he became a Professor ordinarius at the Friedrich-Wilhelms-Universität in Berlin, where he was elected rector in 1858–1859, and again in 1871–1872. In 1849 he also became the director of the Prussian Meteorological Institute.
During his career he published more than 300 papers, some of which delved into experimental physics. He also had an important influence over the science of meteorology, and was considered by some to be a pioneer in this field; Dove's primary meteorological focus was in climatology, a field pioneered by Alexander von Humboldt.
In 1839 he discovered the technique of binaural beats, whereby slightly different frequencies played separately to each ear produced a perception of interference beats at the same rate as would be physically created.
He also studied the distribution of heat over the surface of the Earth, the effect of climate on the growth of plants, and was the first to measure the strength of an electric current in a wire induced by a collapsing magnetic field.