"For God was pleased to have all his fullness dwell in the Son" (Colossians 1:19 NET Bible)
"because God was pleased to have all fullness to dwell in him" (NWT Rev. 2013)
"For in him all the fullness of God was pleased to dwell" (ESV)
"For it pleased the Father that in him should all fullness dwell" (KJV)
From Meyer's NT Commentary:
He was pleased, placuit ei, that, etc. As to this use of εὐδοκεῖν in the later Greek (1 Corinthians 1:21; Galatians 1:15, et al.), for which, in the classical language, δοκεῖν merely was employed, see Fritzsche, ad Rom. II. p. 370. On the accusative with infinitive, comp. 2Ma 14:35; Polyb. i. 8. 4. The subject, whose pleasure it is, is not expressed; but that it is God, is obvious from the context, which in ἵνα γένηται κ.τ.λ. has just stated the divine purpose. Among Greek authors also ὁ Θεός is not unfrequently omitted, where it is self-evident as the subject. See Kühner, II. 1, p. 30 c.
From the Cambridge Bible:
Grammatically, the Greek admits three possible explanations: (a) "For in Him all the Plenitude was pleased to take up Its abode;" (b) "For He (the Son) was pleased that all the Plenitude should take up Its abode in Him;" (c) "For He (God, the Father) was pleased that all the Plenitude should take up Its abode in Him (the Son)." What decision does the context, or other side-evidence, indicate? The explanation (b) is discredited as assigning to the Son a determining choice which the whole context leads us to assign to the Father. The explanation (a), adopted and ably defended by Ellicott, is that of the Old Latin Version. It is grammatically simple, and it is capable of doctrinal defence; "the Plenitude" of the Divine Nature being taken to include the actings of the Divine Will as the expression of the Nature, and so to signify the Divine Personality (here, of course, that of the Father). But it is in itself a surprising and extremely anomalous expression; and it becomes still more so when we read on, and see what are the actions attributed to the same Subject, and that the Subject appears in the masculine gender in the word rendered "having made peace" (see note below), while the word Plerôma (Plenitude) is neuter. On the whole we believe (c) to be the true explanation, with Alford, and Lightfoot, who compares James 1:12; James 4:6 (the better supported reading in each case); "the crown which He (unnamed) promised;" "the Spirit which He (unnamed) caused to dwell in us." He points out also that the noun (eudokia) kindred to the verb here is often, and almost as a habit, used of God's "good pleasure" where God is not named.
Εὐδόκησε, He was well-pleased) viz. God [Engl. Vers. the Father]. This must be supplied, in accordance with the mind of Paul, who, while he mentions the benefit conferred by Christ, never fails to remember the Father. As to the Father’s being well-pleased in the Son, comp. Matthew 3:17 : For εὐδοκῶ with the accusative and infinitive following, see 2Ma 14:35. Moreover, on ΕὐΔΌΚΗΣΕ, He has been well-pleased, depend to reconcile, and having made peace.—πᾶν τὸ πλήρωμα, all the fulness) ch. Colossians 2:9-10; Colossians 2:2, Colossians 4:12; Colossians 4:17, Colossians 1:9; Colossians 1:25; Ephesians 1:23, note. Who can fathom the depth of this subject?
John Eadie's Commentary on Colossians:
῞οτι ἐν αὐτῷ εὐδόκησεν. A different spelling of the word is exhibited in some of the MSS. such as A, D, E,- ηὐδόκησεν, but without authority. Schmid supposes that πλήρωμα is the nominative; and he understands it thus-the entire Godhead was pleased to dwell in Christ. We believe, with the majority of expositors, that ὁ θεός is to be supplied as the nominative, and not τῷ θεῷ, in the dative. Matthew 3:17; Luke 3:22. The full syntax is found in 1 Corinthians 1:21; Galatians 1:15. But we cannot hold, with some, that the pronoun αὐτῷ refers to God, for we take it as still pointing to Him who has been the prime subject of discourse. To make ὁ χριστός the nominative, as Conybeare does, implies the sense that Christ is not only the means, but the end in this reconciliation, for the reading would plainly be in the next verse—“and by Himself to reconcile all things unto Himself,” a mode of speech not in accordance with Pauline usage. Christ reconciles, not to Himself, but to God. We incline also to connect the clause immediately with the preceding one, and not generally with the previous paragraph. "That in all things He might have the pre-eminence;" for, in order to this, “it pleased God-it was His good purpose-that in Him should all fulness dwell.” The pre-eminence, therefore, could not but be His. The verb does not mean that it was God's desire that all fulness should dwell in Christ, but that it was His resolve, as being His pleasure.
NET Bible Notes:
The noun "God" does not appear in the Greek text, but since God is the one who reconciles the world to himself (cf. 2 Cor 5:19), he is clearly the subject of εὐδόκησεν (eudokhsen).