The systems of satellites and rings surrounding the giant planets in the Solar System have remarkably similar architectures. Closest to each planet are rings with associated moonlets, then larger `regular' satellites on nearly circular orbits close to the planet's equatorial plane, and finally one or more distant, small `irregular' satellites on highly elliptical or inclined orbits. Hitherto, the only departure from this broad classification scheme was the satellite system around Uranus, in which no irregular satellites had been found. Here we report the discovery of two satellites orbiting Uranus at distances of several hundred planetary radii. These satellites have inclined, retrograde orbits of moderate eccentricity that clearly identify them as irregular. The satellites are extremely faint (apparent red magnitudes mR = 20.4 and 21.9), with estimated radii of only 60 and 30km. Both moons are unusually red in colour, suggesting a link between these objects-which were presumably captured by Uranus early in the Solar System's history-and other recently discovered bodies orbiting in the outer Solar System.