He taught in Lausanne, where he became a Calvinist, before moving to Utrecht in 1751, and then Berlin in 1763, where he remained for the rest of his life. In 1745, he married Elizabeth du Fresne with whom he had three children, the only surviving child was Maximilian Friedrich Gustav Adolf Salvemini (see below). In 1757, Elizabeth died, and he married Madeleine Raven two years later. In November 1787 he suffered a stroke. He met the Scottish diarist James Boswell in both Utrecht and Berlin, with Boswell recording several anecdotes and conversations.
In 1745, he was elected to the Royal Society. In 1765, Frederick the Great appointed him "Astronomer Royal", of the Observatory of Berlin. He received additional honors from foreign academies, was appointed a member of the Academy of Bologna in 1768, the Academy of Mannheim in 1777, the Academy of Padua in 1784, and the Academy of Prague in 1785. Succeeding Joseph-Louis Lagrange, he was appointed Director of the Mathematics Section of the Berlin Academy, a role he held until his death.