Einstein presented the final form of the general theory of relativity in 1915.
The decisive event was a series of presentations to the Prussian Academy of Sciences in November 1915. On 25 November, Einstein gave the field equations in the form still used today: the Einstein tensor, or equivalently the Ricci tensor minus one-half the metric times the Ricci scalar, equals the stress-energy tensor multiplied by a constant.
The date marks the completion of the theory’s field equations, not the end of every publication or experimental test. Einstein had been developing a relativistic theory of gravity since 1907, and the work involved collaborations and intellectual exchanges with figures including Marcel Grossmann, Tullio Levi-Civita, and David Hilbert.
A major historical complication is that Einstein’s October 1915 equations were not yet correct in their final form. They produced important results, including Mercury’s anomalous perihelion advance, but had conservation problems. Einstein corrected them during November. The completed theory was then presented in a fuller published exposition in 1916, which is why 1915 and 1916 can both appear in historical accounts.