Wolf, the son of a reformed pastor, studied physics and astronomy at the University of Zurich, in Vienna, Berlin and Paris from 1833. After his studies, Wolf became a teacher of mathematics and physics at the Realschule in Berne in 1839, a private lecturer in 1844 and chairman of the observatory in Berne in 1847, and associate professor at the University of Berne in 1853. In 1855 he went to the upper secondary school in Zurich as a teacher of mathematics (which he was until 1861) and was simultaneously professor of astronomy at the Polytechnic (today's ETH Zurich) and at the University of Zurich. He also directed the library of the ETH Zurich. He held these positions until his death.
An important scientific contribution was the exact determination of the period of about 11 years within which the number of sunspots fluctuates. In 1849, he developed a method to record sunspot activity. According to him, this measure for the relative frequency of sunspots is also called Wolf's Relative Number. In 1832, he had already established a connection between the daily fluctuation of the movement of magnetic needles and sunspot number. In 1852, he and others independently determined that the cycle of sunspot activity coincided with that of the Earth's magnetic field. The Zurich sunspot observation series founded by him are considered to be the oldest such series of measurements that have been carried out continuously up to the present. Wolf made his comprehensive auroral data available to his friend Hermann Fritz, which served as the basis for his "Directory of Observed Auroras". From these compilations the parallelism of solar, geomagnetic and auroral activity was derived.
He was also a science historian, published books on the history of astronomy and four volumes of biographies on the cultural history of Switzerland, which he supplemented with numerous articles in journals. Wolf was a very productive writer. Among other things, his history of surveying in Switzerland is still quoted today. He was president of the Geodetic Commission of Switzerland from 1861 to 1893 and participated in a new precision survey of Switzerland. He was also a pioneer of meteorology in Switzerland and was a member of the Swiss Meteorological Commission since its foundation in 1861. From 1866 to 1881 he was its president and first director of the Central Meteorological Institute of Switzerland.
In 1850 he carried out extensive series of measurements on Buffon's needle problem. For 38 years, from 1856 to 1893, Wolf was editor of the quarterly journal of the Naturforschenden Gesellschaft in Zurich. Before that, he published the Mittheilungen der Naturforschenden Gesellschaft in Bern from 1843 to 1855. From 1841 to 1854 he was secretary of the Naturforschenden Gesellschaft Bern.
In 1864, he became a member of the Royal Astronomical Society in London and in 1885 a corresponding member of the Académie des Sciences. The Naturforschende Gesellschaft zu Emden appointed Johann Rudolf Wolf as a corresponding honorary member in 1870. In 1852 he received an honorary doctorate in Bern.