Herschel was born in Slough, Buckinghamshire, the son of Mary Baldwin and astronomer Sir William Herschel. He was the nephew of astronomer Caroline Herschel. He studied shortly at Eton College and St John's College, Cambridge, graduating as Senior Wrangler in 1813. It was during his time as an undergraduate that he became friends with the mathematicians Charles Babbage and George Peacock. He left Cambridge in 1816 and started working with his father. He took up astronomy in 1816, building a reflecting telescope with a mirror  in diameter, and with a  focal length. Between 1821 and 1823 he re-examined, with James South, the double stars catalogued by his father. He was one of the founders of the Royal Astronomical Society in 1820. For his work with his father, he was presented with the Gold Medal of the Royal Astronomical Society in 1826 (which he won again in 1836), and with the Lalande Medal of the French Academy of Sciences in 1825, while in 1821 the Royal Society bestowed upon him the Copley Medal for his mathematical contributions to their Transactions. Herschel was made a Knight of the Royal Guelphic Order in 1831. He also seemed to be aware of Indian thought and mathematics introduced to him by George Everest as claimed by Mary Boole:
He stated in his historical article Mathematics in Brewsters Cyclopedia':
Herschel served as president of the Royal Astronomical Society three times: 1827–1829, 1839–1841 and 1847–1849.
Herschels A preliminary discourse on the study of natural philosophy, published early in 1831 as part of Dionysius Lardners Cabinet cyclopædia, set out methods of scientific investigation with an orderly relationship between observation and theorising. He described nature as being governed by laws which were difficult to discern or to state mathematically, and the highest aim of natural philosophy was understanding these laws through inductive reasoning, finding a single unifying explanation for a phenomenon. This became an authoritative statement with wide influence on science, particularly at the University of Cambridge where it inspired the student Charles Darwin with "a burning zeal" to contribute to this work.
He was elected as a member to the American Philosophical Society in 1854.
Herschel published a catalogue of his astronomical observations in 1864, as the General Catalogue of Nebulae and Clusters, a compilation of his own work and that of his fathers, expanding on the senior Herschels Catalogue of Nebulae. A further complementary volume was published posthumously, as the General Catalogue of 10,300 Multiple and Double Stars.
Herschel correctly considered astigmatism to be due to irregularity of the cornea and theorised that vision could be improved by the application of some animal jelly contained in a capsule of glass against the cornea. His views were published in an article entitled Light in 1828 and the Encyclopædia Metropolitana in 1845.
Discoveries of Herschel include the galaxies NGC 7, NGC 10, NGC 25, and NGC 28.