On November 1, 1950, Pope Pius XII solemnly declared:
44. For which reason, after we have poured forth prayers of supplication again and again to God, and have invoked the light of the Spirit of Truth, for the glory of Almighty God who has lavished his special affection upon the Virgin Mary, for the honor of her Son, the immortal King of the Ages and the Victor over sin and death, for the increase of the glory of that same august Mother, and for the joy and exultation of the entire Church; by the authority of our Lord Jesus Christ, of the Blessed Apostles Peter and Paul, and by our own authority, we pronounce, declare, and define it to be a divinely revealed dogma: that the Immaculate Mother of God, the ever Virgin Mary, having completed the course of her earthly life, was assumed body and soul into heavenly glory.
(from the Apostolic Constitution Munificentissimus Deus)
Thus, the Assumption of Mary was dogmatically defined in 1950. It was clear though, that the belief was already commonly held throughout the church since the earliest days of Christianity.
Here is an excerpt from Catholic Answers which explains this development:
Neither Jerome, Origen, Athanasius, Ambrose, nor Augustine contested Epiphanius in what he had written regarding Mary's miraculous passing, and Ephraem (d. 373) described Mary as having been glorified by Christ and carried through the air to heaven (Cf. Ephraem, De nativitate domini sermo 12, sermo 11, sermo 4; Opera omni syriace at latine, Vol. 2, 415). Throughout history, there have been very few opponents in the Church of Mary's Assumption. No one seemed ready to claim that she corrupted. In fact, the first opposition to the Assumption cannot be found until Ambrosius Autpertus of the eighth century.
From this faith of the Church, Christians began to celebrate the feast of Mary's unique passing. Like the fruit from a tree, the liturgy is the result of doctrine, not the source of it. By the end of the fourth century, the feast of the Dormitio or Koimesis, which celebrated Mary's death, resurrection, and Assumption, was celebrated throughout the East. A feast celebrating Mary's entrance to heaven, "The Memory of Mary," also began around the fourth century. The significance of these early feasts cannot be overlooked, as they are testimony to the truths that the Church knew to be true. Christians would not initiate feasts throughout the Church that were ideas on the fringes of Catholic thought.
One reason why it is difficult to assess where Mary's last days were is because she left no remains. The early Church prized the relics of early Christians, as can be seen by reading The Martyrdom of Polycarp. However, no one claimed to have Mary's remains, which would have been prized above all others. There is no historical reference to the relics of Mary, the corruption of Mary, or the place where her body lies. A skeptic who denies Christ's Resurrection should be asked to find evidence of the remains of Christ, and the same challenge can be extended to whoever denies Mary's Assumption.
Again from Munificentissimus Deus:
43. We rejoice greatly that this solemn event falls, according to the design of God's providence, during this Holy Year, so that we are able, while the great Jubilee is being observed, to adorn the brow of God's Virgin Mother with this brilliant gem, and to leave a monument more enduring than bronze of our own most fervent love for the Mother of God.