Goeckingk was born in Gröningen (Landkreis Börde) and went to school in Halberstadt, where he became friends with Johann Wilhelm Ludwig Gleim. He continued his schooling at Halle, where he was a fellow pupil of another noted poet, Gottfried August Bürger. He went to the university of that city and studied book-keeping and jurisprudence. After finishing his studies in 1768 he became Referendar in the War and Territorial Chamber in Halberstadt. From 1770 he was chancellery director in the Prussian settlement of Ellrich, found the time to begin a career as a writer with Lieder zweier Liebenden ("Songs of Two Lovers"), and met his future wife Ferdinande Vogel (d. 1781). Between 1776 and 1779 he helped edit the Göttinger Musenalmanach, and in 1783 he founded the Journals von und für Deutschland. In 1786 he became a councillor in the War and Territorial Chamber in Magdeburg, in 1788 an agricultural tax commissioner in Wernigerode and Prussian commissar, and in 1793 upper privy councillor of finance in Berlin.
Goeckingk was ennobled in 1789 as a reward for successfully putting the affairs of the Royal Abbey of Quedlinburg in order. From this point on he styled himself Goeckingk auf Daldorf und Günthersdorf. After the General Directory in Berlin was dissolved following the Treaty of Tilsit (1807), he made his resignation in 1808 and turned back to poetry. He lived for several years in Wernigerode.
In 1814 he withdrew from his remaining official responsibilities and went into retirement. He lived at first in Berlin, then moved in with his daughter at Groß Wartenberg, now Syców, where he died on 18 February 1828.
