Born in North Stratford, Connecticut, he was the son of Gold Selleck Silliman and his wife née Mary Fish, widow of John Noyes.
He was educated at Yale, receiving an AB degree in 1796 and and AM in 1799. He studied law with Simeon Baldwin from 1798-99 and became a tutor at Yale 1799-1802. He was admitted to the bar in 1802. President Timothy Dwight IV of Yale proposed that he equip himself to teach in chemistry and natural history and accept a new professorship at the university.
Silliman studied chemistry with Professor James Woodhouse in Philadelphia, Pennsylvania and delivered his first lectures in chemistry at Yale in 1804. In 1805 he traveled to Edinburgh for further study.
Returning to New Haven, he studied its geology, and made a chemical analysis of the meteor that fell near Weston, Connecticut, publishing the first scientific account of any American meteor. He lectured publicly at New Haven in 1808 and came to discover many of the constituent elements of many minerals. As professor emeritus he delivered lectures at Yale on geology until 1855; in 1854 he became the first person to fractionate petroleum by distillation.
Silliman was an opponent of slavery and a supporter of Abraham Lincoln. He was the first president of the American Association for the Advancement of Science. He founded and edited the American Journal of Science, and was appointed one of the corporate members of the National Academy of Sciences by the U.S. Congress.
His first marriage was on 17 September 1809 to Harriet Trumbull, daughter of Connecticut governor Jonathan Trumbull, Jr. They had four children: one daughter married Professor Oliver P. Hubbard, and another married Professor James Dwight Dana.
His second marriage was in 1851 to Mrs Sarah Isabella (McClellan) Webb, daughter of John McClellan.
Silliman died at New Haven, Connecticut
One of Yale's residential colleges is named for him.