Those God effectually calls he also freely justifies (Ro 3:24; 8:30). He does this, not by infusing righteousness into them but by pardoning their sins and accounting and accepting them as righteous (Ro 4:5-8; Eph 1:7). He does this for Christ’s sake alone and not for anything produced in them or done by them (1Co 1:30-31; Ro 5:17-19). He does not impute faith itself, the act of believing, or any other gospel obedience to them as their righteousness. Instead, he imputes Christ’s active obedience to the whole law and passive obedience in his death as their whole and only righteousness by faith (Php 3:8-9; Eph 2:8-10). This faith is not self-generated; it is the gift of God (Jn 1:12; Ro 5:17).
Faith that receives and rests on Christ and his righteousness is the only instrument of justification (Ro 3:28). Yet it does not occur by itself in the person justified, but it is always accompanied by every other saving grace. It is not a dead faith but works through love (Gal 5:6; Jas 2:17, 22, 26).
By his obedience and death, Christ fully paid the debt of all those who are justified. He endured in their place the penalty they deserved. By this sacrifice of himself in his bloodshed on the cross, he legitimately, really, and fully satisfied God’s justice on their behalf (Heb 10:14; 1Pe 1:18-19; Isa 53:5-6). Yet their justification is based entirely on free grace, because he was given by the Father for them, and his obedience and satisfaction were accepted in their place. These things were done freely, not because of anything in them (Ro 8:32; 2Co 5:21), so that both the exact justice and the rich grace of God would be glorified in the justification of sinners (Ro 3:26; Eph 1:6-7; 2:7).
From all eternity God decreed to justify all the elect (Gal 3:8; 1Pe 1:2; 1Ti 2:6), and in the fullness of time Christ died for their sins and rose again for their justification (Ro 4:25). Nevertheless, they are not justified personally until the Holy Spirit actually applies Christ to them at the proper time (Col 1:21-22; Tit 3:4-7).
God continues to forgive the sins of those who are justified (Mt 6:12; 1Jn 1:7, 9). Even though they can never fall from a state of justification (Jn 10:28), they may fall under God’s fatherly displeasure because of their sins (Ps 89:31-33). In that condition they will not usually have the light of his face restored to them until they humble themselves, confess their sins, plead for pardon, and renew their faith and repentance (Ps 32:5; 51; Mt 26:75).
In all these ways, the justification of believers under the Old Testament was exactly the same as the justification of believers under the New Testament (Gal 3:9; Ro 4:22-24).