On completing his course he became secretary to Field-Marshal Count Flemming, chief minister to the Elector of Saxony; after a short time, however, he went to Hannover to find a permanent position.
After the death of Leibniz 1716 he was made librarian and historiographer to the House of Hanover, in 1719 he outlined the Protogaea by the geological formation he had noticed in 1718 at the Ernst-August-Canal of the Herrenhausen Gardens.
For reasons which have never been clearly explained he gave up his position, in 1723, and fled from Hanover, perhaps on account of debt, to the Benedictine monastery at Corvey, and thence to the Jesuits at Cologne, where he became a Catholic.
In his work Eckhart was influenced by the new school of French historians, and gave careful attention to the so-called auxiliary sciences, above all to diplomatics; he also strove earnestly to follow a strictly scientific method in his treatment of historical materials.
Besides the help he rendered Leibniz, of whom he edited the Collectanea Etymologica (1717) and prepared an affectionately respectful obituary (in Christoph Gottlieb von Murr, Journal für Kunstgeschichte, VII), he issued a number of independent works.