From the Sacramentary:
When the people are gathered, the Priest approaches the altar with the ministers while the Entrance Chant is sung.
When he has arrived at the altar, after making a profound bow with the ministers, the Priest venerates the altar with a kiss and, if appropriate, incenses the cross and the altar. Then, with the ministers, he goes to the chair.
When the Entrance Chant is concluded, (see, the Chant doesn’t have to stop the second he reaches sanctuary – or even the chair), the Priest and the faithful, standing, sign themselves with the Sign of the Cross, while the Priest, facing the people, says:
There would be no reason for him to go to the chair at all if everything were to be done at the altar. There is actually no mention of the priest at the altar until the Liturgy of the Eucharist.