The Lense-Thirring effect, a tiny perturbation of the orbit of a particle caused by the spin of the attracting body, was accurately measured with the use of the data of two laser-ranged satellites, LAGEOS and LAGEOS II, and the Earth gravitational model EGM-96. The parameter mu, which measures the strength of the Lense-Thirring effect, was found to be 1.1 +/- 0.2; general relativity predicts mu = 1. This result represents an accurate test and measurement of one of the fundamental predictions of general relativity, that the spin of a body changes the geometry of the universe by generating space-time curvature.