Geijer was born at Geijersgården, his family's estate in Ransäter, Värmland. He was educated at the gymnasium of Karlstad and then attended the University of Uppsala, where he earned his master's degree in 1806. In 1803 he had competed successfully for an historical prize offered by the Academy of Sciences at Stockholm. In 1809, he traveled in England. The year following, he became a lecturer in history at Uppsala, and in 1815 assistant to Eric Michael Fant. Succeeding Fant, Geijer was a professor of history from 1817 at Uppsala University where a statue now commemorates him. He was rector of Uppsala University during the years 1822, 1830, 1836 and 1843–1844. As a representative of the university, he was a member of the Church of Sweden clergy: 1828-30 and 1840–41. He was a member of the Swedish Academy (on seat 14) from 1824. In 1835, he became a member of the Royal Swedish Academy of Sciences.