Justified sinners are those called by God's grace who, through faith in Christ alone, receive God's imputation to them of the satisfaction of Jesus's atoning death and righteous obedience, which for Christ's sake are accounted - credited - reckoned to them as righteousness for their unqualified pardon and acceptance before God as if really performed by them; not a righteousness infused or worked inherently into them, but imputed to them.
Heidelberg Catechism 60 Although my conscience accuses me that I have grievously sinned against all God's commandments, have never kept any of them, and am still inclined to all evil, yet God, without any merit of my own, out of mere grace, imputes to me the perfect satisfaction, righteousness, and holiness of Christ. He grants these to me as if I had never had nor committed any sin, and as if I myself had accomplished all the obedience which Christ has rendered for me, if only I accept this gift with a believing heart.
Belgic Confession 22 Jesus Christ, imputing to us all his merits and so many holy works which he has done for us, and in our stead, is our Righteousness.
Westminster Confession of Faith 11.1 Those whom God effectually calls, He also freely justifies; not by infusing righteousness into them, but by pardoning their sins, and by accounting and accepting their persons as righteous; not for any thing wrought in them, or done by them, but for Christ's sake alone; nor by imputing faith itself, the act of believing, or any other evangelical obedience to them, as their righteousness; but by imputing the obedience and satisfaction of Christ unto them.
Westminster Larger Catechism 71 Although Christ, by his obedience and death, did make a proper, real, and full satisfaction to God's justice in the behalf of them that are justified; yet inasmuch as God accepts the satisfaction from a surety, which he might have demanded of them, and did provide this surety, his own only Son, imputing his righteousness to them, and requiring nothing of them for their justification but faith, which also is his gift, their justification is to them of free grace.
Westminster Shorter Catechism 33 Justification is an act of God's free grace, wherein he pardons all our sins, and accepts us as righteous in his sight, only for the righteousness of Christ imputed to us, and received by faith alone.
Article XI Of the Justification of Man We are accounted righteous before God, only for the merit of our Lord and Saviour Jesus Christ by Faith, and not for our own works or deservings; Wherefore, that we are justified by Faith only is a most wholesome Doctrine, and very full of comfort, as more largely is expressed in the Homily of Justification.