[The following are excerpts from the Catholic Encyclopedia's entry on "clerical costume" and deals with the development of the Roman cassock as clerical dress. 
The canons of the Council of Braga in Portugal (572) required the clergy to wear a vestis talaris, or tunic, reaching to the feet, and even in far-off Britain we find indications, both among the Celts and Anglo-Saxons, that undraped lower limbs were not regarded as seemly in the clergy, at any rate during their service at the altar. During the same period synodal decrees became gradually more frequent, restraining in various ways the tendency of the clergy to adopt the current fashion of worldly attire. [...] Perhaps the most interesting and significant enactment of this period is a letter of Pope John VIII (c. 875) admonishing the Archbishops of Canterbury and York to see that their clergy wore due ecclesiastical attire, and quoting the example of the English clergy in Rome who, on the eve of St. Gregory's feast, had given up their short cloaks and adopted the long Roman tunic reaching to the feet...
In the later Middle Ages the dress of the clergy was regulated by the canon law, the jus commune of the Church at large, but with many supplementary enactments passed by local synods. The Fourth Lateran Council (1215) laid down the principle that clerics must wear garments closed in front and free from extravagance as to length... Ornamental appendages, cloth of red or green colour, brooches (fibulœ) to fasten their cloaks, and the wearing of sleeved copes (cappœ manicatœ), either at Office or at other times, are all forbidden by the same enactment... In 1237 the national council, held under the presidency of the Legate Otho, declared that lay folk were scandalized at the dress of the clergy, which was not clerical at all, but more suited to knights (non clericalis sed potius militaris). Offenders in future were to be punished, and the bishops were to see that all in sacred orders used garments of fitting length and wore closed copes. Somewhat later the legatine council under Ottoboni insisted that all ecclesiastics, whether in Sacred orders or not, were to wear clothes of fitting length, coming at any rate below the middle of the shin (saltem ultra tibiarum medium attingentes). Further, all priests and beneficed clergy were to wear closed copes, except when on a journey, or for some other just reason (Wilkins, "Concilia", II, 4)... The proper dress of the medieval clergy was therefore the vestis talaris, and over this priests and dignitaries were bidden to wear the cappa clausa. The former of these must have been a sort of cassock, but made like a tunic, i. e. not opening, and buttoning down the front...
Modern Usage
The modern and more centralized legislation regarding clerical costume may be considered to begin with a constitution of Sixtus V, in 1589, insisting under the severest penalties that all clerics, even those in minor orders, should uniformly wear the vestis talaris and go tonsured.
The decrees on the subject of the First Synod of Westminster and the Third Plenary Council of Baltimore are in practical agreement. The latter says (?77), "We wish therefore and enjoin that all keep the law of the Church, and that when at home or when engaged in the sanctuary they should always wear the cassock [vestis talaris] which is proper to the clergy. When they go abroad for duty or relaxation, or when upon a journey, they may use a shorter dress, but still one that is black in colour, and which reaches to the knees, so as to distinguish it from lay costume. We enjoin upon our priests as a matter of strict precept, that both at home and abroad, and whether they are residing in their own diocese or outside of it, they should wear the Roman collar."
[For the sake of further interest. Compare this with the Eastern "rason", which is basically the same kind of black tunic garment:
