For those whom he foreknew he also predestined to be conformed to the image of his Son, in order that he might be the firstborn among many brothers. And those whom he predestined he also called, and those whom he called he also justified, and those whom he justified he also glorified. (Rom 8:29-30)
In other words, those who God knew were predestined to Christ-likeness. Then in verse 30, Paul shows us the golden chain of salvation. Those who are foreknown are predestined, those He predestines He calls, those He calls He justifies, those He justifies He glorifies. Each link in our salvation is dependent on the previous link, which makes all of salvation dependent, primarily, on God, and secondarily, His election.
So then, we see that the purpose of election is glorification, or, Christ-likeness. Paul says the same thing in Ephesians;
"...even as he chose us in him before the foundation of the world, that we should be holy and blameless before him. " (Eph 1:4)
So, since we know that God intends to make us like Christ, the question becomes, "How does He do it?" Good question! Here's your answer.
I guess we need to be a little more technical in our answer. He does it by sending Christ to live a perfect life and die in our place as though He had lived our wicked life, raising Him from the dead, giving the Holy Spirit, sending preachers into all the world, calling the elect through the preaching of the Gospel, regenerating the elect, sanctifying the elect, and keeping them till that day when we see Jesus face to face and are transformed into His likeness.
But we are not to think that Christ-likeness is only something that is accomplished in the future. Christ-likeness is something that is being accomplished now in our lives. This is called sanctification. Sanctification is the process whereby we are being conformed to Christ's image right now. This is an area where we are challenged by Scripture. If we are not being sanctified, we are not saved. Paul tells us this in 2 Thessalonians;
But we ought always to give thanks to God for you, brothers beloved by the Lord, because God chose you as the firstfruits to be saved, through sanctification by the Spirit and belief in the truth. To this he called you through our gospel, so that you may obtain the glory of our Lord Jesus Christ. (2Th 2:13-14)
Sanctification is the means that God has ordained to bring us to the glory of our Lord Jesus Christ. This is why the matter of sanctification is vitally important to diagnosing our spiritual health. If there is no sanctification present, you are dead. God chose us to be like Christ, and all those He chose must be conformed to the image of Christ.
This conforming to the image of Christ takes place as we hear and obey the Word. As we gaze intently into the Scriptures we see Jesus. We are being transformed into His glory. This does not happen for everyone who reads the Bible, though. It is only after the veil has been removed from our eyes that we can see Christ in the Scriptures. Paul, again tells us this in 2 Corinthians;
But when one turns to the Lord, the veil is removed. Now the Lord is the Spirit, and where the Spirit of the Lord is, there is freedom. And we all, with unveiled face, beholding the glory of the Lord, are being transformed into the same image from one degree of glory to another. For this comes from the Lord who is the Spirit. (2Co 3:16-18)
Only by the work of the Spirit opening our eyes to Christ are we able to see Him. And as we see Him we are changed. And when we finally see Him face to face we will be changed.
Behold! I tell you a mystery. We shall not all sleep, but we shall all be changed, in a moment, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, and the dead will be raised imperishable, and we shall be changed. For this perishable body must put on the imperishable, and this mortal body must put on immortality. When the perishable puts on the imperishable, and the mortal puts on immortality, then shall come to pass the saying that is written: "Death is swallowed up in victory." "O death, where is your victory? O death, where is your sting?" The sting of death is sin, and the power of sin is the law. But thanks be to God, who gives us the victory through our Lord Jesus Christ. Therefore, my beloved brothers, be steadfast, immovable, always abounding in the work of the Lord, knowing that in the Lord your labor is not in vain. (1Co 15:51-58)
Beloved, we are God's children now, and what we will be has not yet appeared; but we know that when he appears we shall be like him, because we shall see him as he is. And everyone who thus hopes in him purifies himself as he is pure. (1Jo 3:2-3)
God's purpose in choosing us is that we should be holy, blameless, sanctified, and conformed to the image of Christ. And if God has chosen, we can rest assured that it will be accomplished.
Soli Deo Gloria