The classical planets are Saturn, Jupiter, Mars, the Sun, Venus, Mercury and the Moon, and they take rulership over the hours in this sequence.
The sequence is from slowest- to fastest-moving as the planets appear in the night sky, and so is from furthest to nearest in the planetary spheres model.
The astrological order of the days was explained by Vettius Valens and Dio Cassius (and Chaucer gave the same explanation in his Treatise on the Astrolabe).
The Ptolemaic system of planetary spheres asserts that the order of the heavenly bodies, from the farthest to the closest to the Earth is: Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon (or, objectively, the planets are ordered from slowest to fastest moving as they appear in the night sky – note however that the sun, Venus, and Mercury all advance by 360° per year, on average).
According to Vettius Valens, the first hour of the day began at sunset, which follows Greek and Babylonian convention.