When it is said
At every Divine Liturgy the Gospel is announced, and the people answer with these words. Then the reading begins.
When it ends, the priest greets the reader with peace, and the people sing the same words again.
The same is sung at Matins, the morning service, when the priest reads the Gospel.
Where it comes from
No author known
As the Gospel begins
At the Liturgy the call comes first: “Wisdom! Let us listen to the holy Gospel.” The deacon names the Gospel to be read, from Matthew, Mark, Luke or John. Before a word of it is read, the people sing: “Glory to You, O Lord, glory to You.”
And again when it ends
When the reading is over, the priest says to the one who read it: “Peace be with you, who proclaim the good news.” The people sing the same words once more. In the Greek of the Liturgy they are “Doxa si, Kyrie, doxa si”, and they come at the same two moments.
Isabel F. Hapgood, Service Book (1906): the Divine Liturgy; The Divine Liturgy in Greek (Greek Orthodox Archdiocese of America)
In Greek
Δόξα Σοι, Κύριε, δόξα Σοι.