Substitutionary atonement is the sacrifice Christ made for the sins of the whole world (Jn.3:16). Those who repent and put their faith in Christ alone for salvation (Eph. 2:8-9) will receive the righteousness of Christ. The righteousness of Christ is imputed or given to believers. “God made him who had no sin to be sin for us so that in him we might become the righteousness of Christ (2 Cor. 5:21).” The reason Christ could be our substitute and impute his righteousness was that he perfectly obeyed the will of God the Father. He is the perfect standard of the love and justice of God that was required for humankind to be reconciled to God.
Furthermore, substitutionary atonement not only comprises Christ imputing his righteousness to us. It’s important to understand that God was also sent to be the “propitiation” for believers (Rom. 3:25). Propitiation is a sacrifice that bears all God’s wrath on sin. Since God is just and can’t ignore the sins committed by humankind, He chose to sacrifice His only begotten Son. We must remember that Christ voluntarily chose to take the wrath of God and that this wrath was what satisfied the demands of his own righteousness and justice. Thus, atonement is both God giving us His righteousness and appeasing the wrath of God.
The implications of this doctrine for human guilt over sin is crucial. Because Jesus bore our penalty—penal substitution, He became our representative. By becoming our representative, God penalized his only Son instead of us. When we come into a relationship with Jesus, the Bible says “there is therefore now no condemnation (Rom. 8:1).” Since there is no condemnation, Christians who struggle with false guilt should remind Satan, who is the accuser of the brethren, that the sins of mankind were paid in full by Jesus of Nazareth.
Even though we deserve to die for the penalty of our sins and warrant the wrath of God for eternity, Christ, because of his love and mercy, reconciled us through His substitutionary atonement. He brought us back into fellowship with God. The Bible says that “in Christ, God was reconciling the world to himself (2 Cor. 5:18-19).” This is the greatest news in the world. Heaven is a free gift given to us by God, but we should never forget that God bought it in full for us when he suffered on the cross for our sins. Praise Jesus for His grace.
 Wayne Grudem, Systematic Theology, p.569.