Laser-ranging provides some of the most precise tests of gravity in the weak-field regime, enabling experimental probes of Einstein’s general theory of relativity using the Earth as a laboratory1. A central test of general relativity is the amplitude of frame-dragging, that is, the dragging of spacetime by a rotating mass2–5. Owing to its optimized orbit, a very low surface-to-mass ratio and a highly uniform retroreflector distribution, we show that the recently launched Laser Relativity Satellite 2 (LARES-2)6—together with its predecessor LAGEOS and the GRACE satellites—enables a measurement of terrestrial frame-dragging with a relative uncertainty at the one-part-in-a-thousand level, representing an order-of-magnitude improvement over previous Solar System determinations. This result provides a stringent confirmation of general relativity in the near-Earth environment and places strong constraints on alternative gravitational models that predict deviations specifically in frame-dragging, including scalar–tensor extensions such as Chern–Simons gravity7,8. Beyond tests of fundamental physics, the combined analysis of LARES-2 and LAGEOS also improves the determination of Earth’s lunisolar tides, illustrating the broader geophysical impact of high-precision relativistic satellite experiments.