Explanation from Raghunandan from the Planetary Society, India:
The order of the constellations of the Zodiac (as given by the apparent motion of the Sun over a year) starting with the Vernal Equinox and proceeding eastward along the Ecliptic is
The Constellations of the Zodiac :
The ancients observed that the Sun, Moon and those 5 funny wandering stars (the planets known to the ancients) seem to be constrained to a particular region of the sky, never traveling really far north or south of a wide band of stars. They divided this sky band into 12 sections based on the old constellations, each differing in width but all of them about 16° high (+8°/-8°) and called them the “Zodiac”. Each division is named for the constellation situated within its limits in the 2nd century B.C.!
The name “Zodiac” is derived from the Greek, meaning “animal circle” (also related to the word “zoo”), and it comes from the fact that most of these constellations are named for animals, such as Leo, the Lion, Taurus, the Bull and Cancer, the Crab. It turns out that this band of the sky is centered on a line called the “ecliptic” which is the apparent path the Sun appears to take through the sky as a result of the Earth’s revolution around it (actually, it is defined as the projection the Earth’s orbital plane into outer space). If we could see the stars in the daytime, we would see the Sun slowly wander from one constellation of the Zodiac to the next, making one complete circle around the sky in one year. Which constellation the Sun was in had to be inferred by drawing all the constellations, then noting which was the last to set before sunrise and which was the first to rise after sunset then assuming the Sun was half way in between.