David delivered first this psalm - I believe the meaning of this place to be this: David made the psalm on the occasion above specified; and delivered it to Asaph, who was the musician, and to his brethren, to be sung by them in honor of what God had done in behalf of his people.

Then on that day David (c) delivered first [this psalm] to thank the LORD into the hand of Asaph and his brethren.
(c) David gave them this Psalm to praise the Lord, signifying that in all our enterprises the Name of God should be praised and called upon.

Then on that day,.... The ark was brought to Zion, and the above persons appointed to minister before it:
David delivered first this psalm to thank the Lord into the hand of Asaph and his brethren to be sung by them now, and on every proper occasion; and this seems to be the first that was delivered to them; afterwards there were many more, as the titles of the psalms show; the following is composed of part of two others, as they now stand in the book of Psalm. From hence, to the end of 1-Chronicles 16:22 is the same with Psalm 105:1, with a little variation, see the notes there; and from thence to the end of 1-Chronicles 16:33 is Psalm 96:1 which see; and 1-Chronicles 16:34 is the same with Psalm 106:1, see the notes there. See Gill on Psalm 106:1, Psalm 107:1, Psalm 105:1, Psalm 105:2, Psalm 105:3, Psalm 105:4, Psalm 105:5, Psalm 105:6, Psalm 105:7, Psalm 105:8, Psalm 105:9, Psalm 105:10, Psalm 105:11,on Psalm 105:12, Psalm 105:13, Psalm 105:14,on Psalm 105:15

Let God be glorified in our praises. Let others be edified and taught, that strangers to him may be led to adore him. Let us ourselves triumph and trust in God. Those that give glory to God's name are allowed to glory in it. Let the everlasting covenant be the great matter of our joy his people of old, be remembered by us with thankfulness to him. Show forth from day to day his salvation, his promised salvation by Christ. We have reason to celebrate that from day to day; for we daily receive the benefit, and it is a subject that can never be exhausted. In the midst of praises, we must not forget to pray for the servants of God in distress.

HIS PSALM OF THANKSGIVING. (1Ch. 16:7-43)
Then on that day David delivered first this psalm--Among the other preparations for this solemn inauguration, the royal bard had composed a special hymn for the occasion. Doubtless it had been previously in the hands of Asaph and his assistants, but it was now publicly committed to them as they entered for the first time on the performance of their sacred duties. It occupies the greater part of this chapter (1Ch. 16:8-36), and seems to have been compiled from other psalms of David, previously known to the Israelites, as the whole of it will be found, with very slight variations, in Psalm 96:1-13; Psalm 105:1-15; Psalm 106:47-48. In the form, however, in which it is given by the sacred historian, it seems to have been the first psalm given for use in the tabernacle service. Abounding, as it does, with the liveliest ascriptions of praise to God for the revelation of His glorious character and the display of His marvellous works and containing, as it does, so many pointed allusions to the origin, privileges, and peculiar destiny of the chosen people, it was admirably calculated to animate the devotions and call forth the gratitude of the assembled multitude.

On that day David first committed it to Asaph and his sons to give thanks to Jahve. נתן is to be connected with בּיד, which is separated from it by several words, and denotes to hand over to, here to commit to, to enjoin upon, since that which David committed to Asaph was the carrying out of a business which he enjoined, not an object which may be given into the hand. ההוּא בּיּום is accented by אז. בּראשׁ, "at the beginning," "at first," to bring out the fact that liturgical singing was then first introduced. אחיו, the brethren of Asaph, are the Levites appointed to the same duty, whose names are given in 1-Chronicles 16:5, 1-Chronicles 16:6. But in order to give a more exact description of the ליהוה הודות committed to Asaph in vv. 8-36, a song of thanks and praise is given, which the Levites were to sing as part of the service with instrumental accompaniment. It is not expressly said that this song was composed by David for this purpose; but if Asaph with his singers was to perform the service committed to him, he must have been provided with the songs of praise (psalms) which were necessary for this purpose; and if David were in any way the founder of the liturgical psalmody, he, as a richly endowed psalm-singer, would doubtless compose the necessary liturgical psalms. These considerations render it very probable that the following psalm was a hymn composed by David for the liturgical song in the public worship. The psalm is as follows: -
8 Give thanks unto Jahve; preach His name;
Make known His deeds among the peoples:
9 Sing to Him, play to Him;
Meditate upon all His wondrous works.
10 Glory ye in His holy name:
Let the heart of them rejoice that seek the Lord.
11 Seek ye the Lord, and His strength;
Seek His face continually.
12 Remember His wonders which He has done;
His wondrous works, and the judgments of His mouth;
13 O seed of Israel, His servants,
Sons of Jacob, His chosen.
14 He, Jahve, is our God;
His judgments go forth over all the earth.
15 Remember eternally His covenant,
The word which He commanded to a thousand generations:
16 Which He made with Abraham,
And His oath to Isaac;
17 And caused it to stand to Jacob for a law,
To Israel as an everlasting covenant;
18 Saying, "To thee I give the land Canaan,
As the heritage meted out to you."
19 When ye were still a people to be numbered,
Very few, and strangers therein,
20 And they wandered from nation to nation,
From one kingdom to another people,
21 He suffered no man to oppress them,
And reproved kings for their sake:
22 "Touch not mine anointed ones,
And do my prophets no harm."
23 Sing unto Jahve, all the lands;
Show forth from day to day His salvation.
24 Declare His glory among the heathen,
Among all people His wondrous works.
25 For great is Jahve, and greatly to be praised;
And to be feared is He above all the gods.
26 For all the gods of the people are idols;
And Jahve has made the heavens.
27 Majesty and splendour is before Him;
Strength and joy are in His place.
28 Give unto Jahve, ye kindreds of the people,
Give unto Jahve glory and strength.
29 Give unto Jahve the honour of His name:
Bring an offering, and come before His presence;
Worship the Lord in the holy ornaments.
30 Tremble before Him, all the lands;
Then will the earth stand fast unshaking.
31 Let the heavens be glad, and the earth rejoice;
And they will say among the heathen, Jahve is King.
32 Let the sea roar, and the fulness thereof;
Let the field exult, and all that is thereon.
33 Then shall the trees of the wood rejoice
Before the Lord; for He comes to judge the earth.
34 Give thanks unto Jahve, for He is good;
For His mercy endureth for ever.
35 And say, "Save us, God of our salvation:"
And gather us together, and deliver us from the heathen,
To give thanks to Thy holy name,
To glory in Thy praise.
36 Blessed be Jahve, the God of Israel,
From everlasting to everlasting.
And all the people said Amen, and praised Jahve.

First - Hereby it is implied, that after this he delivered many other psalms into their hands, to be sung by them to the praise of God in his public service. We shall find it in the same words, in Psalm 105:1-15 and Psalm 96:1-11, all but the three last verses.