Catechism of the Catholic Church §476 — excerpt
Since the Word became flesh in assuming a true humanity, Christ's body was finite. Therefore the human face of Jesus can be portrayed; at the seventh ecumenical council (Nicaea II in 787) the Church recognized its representation in holy images to be legitimate.
This translation is under copyright, so only the cited words are quoted here. Follow the link for the full text. Translation: English translation of the Catechism of the Catholic Church, 2nd ed. (Libreria Editrice Vaticana), as posted at vatican.va.
Also cites: Council of the Lateran (649): DS 504 · Cal 3:1 · Council of Nicaea II (787): DS 600-603