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:
http://www.newadvent.org/cathen/08253a.htm