This phrase is contained in all three of the oldest Roman Ordines. Ordo Rom I is quoted as saying "When the prayer Post-Communion is over, that one of the deacons appointed by the archdeacon looks towards the pontiff to receive a sign from him and then says to the people: Ite missa est. They answer: Deo gratias" (ed. Atchley, London, 1905, p. 144.) This phrase has also become the technical name for the holy liturgy in the Roman Rite.

In addition to what krimson mentioned above, there is another instance in which the mass is ended with a different phrase. On days of fasting or penance the versicle Ite missa est is replaced by Benedicamus Domino which would still be followed by the same response. This is due to the fact that in early times the people of the church were not dismissed after mass on days of fasting and penance. The people would stay for more prayer and worship thus the differing versicle.

Information drawn from the Catholic Encyclopedia: