Articles 3 and 4 of the Augsburg Confession (part of the Lutheran Confessions) talk about this: The Augsburg Confession (Chief Articles of Faith: Article III: Of the Son of God and Article IV: Of Justification).
Article 3 makes the point that Christ "truly suffered, was crucified, dead, and buried, that He might reconcile the Father unto us, and be a sacrifice, not only for original guilt, but also for all actual sins of men." This is the Atonement; Christ died for our sins (in a similar way, the book of Hebrews also talks about Christ as both the High Priest and the sacrifice, particularly Hebrews 9:11 and following).
Article 4 then talks about justification: "... men cannot be justified before God by their own strength, merits, or works, but are freely justified for Christ's sake, through faith, when they believe that they are received into favor, and that their sins are forgiven for Christ's sake, who, by His death, has made satisfaction for our sins. This faith God imputes for righteousness in His sight. Rom. 3 and 4."
So, we are justified before God when we believe that Christ's sacrifice (the atonement) is for us. That is, we receive the benefits of the atonement, simply by believing that these benefits are for us.
Another way I've heard it put is that it takes one to forgive, but two to reconcile. God forgives us freely due to the sacrifice of Christ (the atonement). But, for us to be reconciled to Him (another way of thinking of justification), we must believe that this forgiveness is ours (i.e. have faith).