With gratitude and with a sure confidence, therefore, let us accept this doctrine, so sweet and so filled with comfort, which teaches that Christ became a curse for us, that is, a sinner worthy of the wrath of God; that He clothed Himself in our person, laid our sins upon His own 
shoulders, and said: “I have committed the sins that all men have committed.” Therefore He truly became accursed according to the Law, not for Himself but, as Paul says, huper hemon [Gk: for us]. For unless He had taken upon Himself my sins, your sins, and the sins of the entire world, the Law would have had no right over Him, since it condemns only sinners and holds only them under a curse. Therefore He could neither have become a curse nor have died, since the cause of the curse and of death is sin, of which He was innocent. But because He took upon Himself our sins, not by compulsion but of His own free will, it was right for Him to bear the punishment and the wrath of God – not for His own Person, which was righteous and invincible and therefore could not become guilty, but for our person.
By this fortunate exchange with us He took upon Himself our sinful person and granted us His innocent and victorious Person. Clothed and dressed in this, we are freed from the curse of the Law, because Christ Himself voluntarily became a curse for us, saying: “For My own Person of humanity and divinity I am blessed, and I am in need of nothing whatever. But I shall empty Myself (Phil. 2:7); I shall assume your clothing and mask; and in this I shall walk about and suffer death, in order to set you free from death.”
Luther’s Works, volume 26 (283-284)