Paul introduced this review of the Gospel with a powerful explanation of Christ's deity:
15 He is the image of the invisible God, the firstborn of all creation. 16 For by him all things were created, in heaven and on earth, visible and invisible, whether thrones or dominions or rulers or authorities—all things were created through him and for him. 17 And he is before all things, and in him all things hold together. 18 And he is the head of the body, the church. He is the beginning, the firstborn from the dead, that in everything he might be preeminent. 19 For in him all the fullness of God was pleased to dwell, 20 and through him to reconcile to himself all things, whether on earth or in heaven, making peace by the blood of his cross. ~~Colossians 1:15-20 (ESV)In describing Christ as "the image of the invisible God," Paul equates Him with God. From there, He identifies Christ's role in creation, insists that He holds the entire universe together, and crowns Him as the Sovereign Ruler. Then he makes his claim even more directly in verse 19: "For in him all the fullness of God was pleased to dwell."
Yes, God dwells in every believer through His Holy Spirit, but He doesn't give us all of His fulness. Vincent's Word Studies offers the clearest commentary on verse 19 that I could find.
The word must be taken in its passive sense - that with which a thing is filled, not that which fills. The fullness denotes the sum-total of the divine powers and attributes. In Christ dwelt all the fullness of God as deity. The relation of essential deity to creation and redemption alike, is exhibited by John in the very beginning of his gospel, with which this passage should be compared. In John the order is: 1. The essential nature of Christ; 2. Creation; 3. Redemption. Here it is: 1. Redemption (Colossians 1:13); 2. Essential being of the Son (Colossians 1:15); 3. The Son as Creator (Colossians 1:16); 4. The Church, with Christ as its head (Colossians 1:18). Compare 2 Corinthians 5:19; Ephesians 1:19, Ephesians 1:20, Ephesians 1:23. Paul does not add of the Godhead to the fullness, as in Colossians 2:9 since the word occurs in direct connection with those which describe Christ's essential nature, and it would seem not to have occurred to the apostle that it could be understood in any other sense than as an expression of the plenitude of the divine attributes and powers.Again, the passage celebrates (rather than merely stating) Christ's divine nature, making it inseparable from the Gospel message. Christ, being God Himself, willingly bled and died on the cross to atone for the sins of those who trust in Him. Remember, Paul here identified Christ as both the Creator and the focal point of His own creation, and in the next breath introduced His willingness to sacrifice Himself for our rebellion against Him. If that amazing fact doesn't give you a desire to fall on your knees with wonder and adoration, just keep reading about the Gospel. It only gets better.
Thus the phrase in Him should all the fullness dwell gathers into a grand climax the previous statements - image of God, first-born of all creation, Creator, the eternally preexistent, the Head of the Church, the victor over death, first in all things. On this summit we pause, looking, like John, from Christ in His fullness of deity to the exhibition of that divine fullness in redemption consummated in heaven (Colossians 1:20-22).