The second consequence attributed to the imputation of Christ’s righteousness, is a title to eternal life. This in the older writers is often expressed by the words “adoption and heirship.” Being made the children of God by faith in Christ Jesus (Gal. 3:26), they are heirs of God and joint heirs with Jesus Christ of a heavenly inheritance. (Romans 8:17.) The mere expiation of guilt confers no title to eternal life. The condition of the covenant under which man was placed was perfect obedience. This, from all that appears in Scripture, the perfection of God requires. As He never pardons sins unless the demands of justice be satisfied, so He never grants eternal life unless perfect obedience be rendered. Heaven is always represented as a purchased possession. In the covenant between the Father and the Son the salvation of his people was promised as the reward of his humiliation, obedience, and death. Having performed the stipulated conditions, He has a claim to the promised recompense. And this claim inures to the benefit of his people. But besides this, as the work of Christ consisted in his doing all that the law of God, or covenant of works requires for the salvation of men, and as that righteousness is freely offered to every one that believes. every such believer has as valid a claim to eternal life as he would have had, had he personally done all that the law demands. Thus broad and firm is the foundation which God has laid for the hopes of his people. It is the rock of ages; Jehovah our righteousness.
—Charles Hodge, Systematic Theology, 3 vols. (Oak Harbor, WA: Logos Research Systems, Inc., 1997), 3.164–65.