Charles Hatchett was born in Long Acre, London to John Hatchett (1729–1806), and Elizabeth Hatchett. John Hatchett was "(one of) the coachbuilders of London of the greatest celebrity". He later became a magistrate in Hammersmith. Charles Hatchett attended a private school, Fountayne's, in Marylebone Park, and was a self-taught mineralogist and analytical chemist.
On 24 March 1786, Charles Hatchett married Elizabeth Martha Collick (1756–1837) at St Martin-in-the-Fields. Their children included:
#John Charles Hatchett (bapt 27 January 1788 St Martin-in-the-Fields)
#His daughter, Anna Frederica Hatchett, married the chemist William Thomas Brande.
Following their marriage, Hatchett and his wife traveled extensively in Poland and Russia for 2 years before settling in Hammersmith.  In 1790, Hatchett again had the opportunity to travel extensively, when his father sent him to deliver a coach to Catherine the Great in St. Petersburg. With an introduction from Sir Joseph Banks, he visited chemist Martin Klaproth, geologist and botanist Peter Pallas, Neapolitan mineralogist Andrea Savaresi, and other scientists.
In 1796 Hatchett took another long tour, this time through England and Scotland, where he visited geological sites, mines, and factories. His diary of this trip was edited by Arthur Raistrick and published in 1967 as  The Hatchett diary: a tour through the counties of England and Scotland in 1796 visiting their mines and manufactories.