I will rejoice and exult in thee. Observe how the faithful praise God sincerely and without hypocrisy, when they do not rest on themselves for happiness, and are not intoxicated with foolish and carnal presumption, but rejoice in God alone; which is nothing else than to seek the matter of their joy from the favor of God, and from no other source, since in it perfect happiness consists. I will rejoice in thee We ought to consider how great is the difference and opposition between the character of the joy which men endeavor to find in themselves, and the character of the joy which they seek in God. David, the more forcibly to express how he renounces every thing which may keep hold of or occupy him with vain delight, adds the word exult, by which he means that he finds in God a full and an overflowing abundance of joy, so that he is not under the necessity of seeking even the smallest drop in any other quarter. Moreover, it is of importance to remember what I have previously observed, that David sets before himself the testimonies of the divine goodness which he had formerly experienced, in order to encourage himself with the more alacrity to lay open his heart to God, and to present his prayers before him. He who begins his prayer by affirming that God is the great source and object of his joy, fortifies himself before-hand with the strongest confidence, in presenting his supplications to the hearer of prayer.

I will be glad - I will rejoice, and will express my joy.
And rejoice in thee - I will exult; I will triumph. That is, he would express his joy in God - in knowing that there was such a Being; in all that he had done for him; in all the evidences of his favor and friendship.
Will sing praise to thy name - To thee; the name often being put for the person.
O thou Most High - Thou who art supreme - the God over all. See the notes at Psalm 7:17.

I will be glad and rejoice in thee - I am glad that thou hast heard my prayer, and showed me mercy; and I will rejoice in thee, in having thee as my portion, dwelling and working in my heart.

I will be glad and rejoice in thee,.... Not in himself, in any attainments or works of his; not in his wisdom, riches, and strength, nor in his warlike exploits, but in the Lord; not in second causes, in horses and chariots, in armies, and in the courage and valour of men, but in God, as the author of deliverance, victory, and salvation; not in God only as the God of nature and providence, but as the God of all grace, and as his covenant God and Father; and because of the blessings of this covenant, as forgiveness of sin, a justifying righteousness, &c. for he rejoiced not in his own righteousness, but in the righteousness of Christ, as well as in his person, grace, and sacrifice; so the Chaldee paraphrase renders it, "I will be glad and rejoice", "in thy Word", the Logos, the essential Word of God, of whom there were many types, promises, and prophecies in the former dispensation; two words being here used express the greatness of this joy, and especially the latter word denotes a very vehement joy, a joy unspeakable and full of glory; such as arises from a sight of Christ the object, and which the psalmist had now in view; and this was not a carnal and worldly joy, but joy in the Holy Ghost;
I will sing praise to thy name, O thou most High; that is, to the glory of his name, his being, and perfections, as displayed in his marvellous works, and in the revelation of his word, and especially in his son; and under the character of the "most high" God, the supreme Being over all creatures, angels and men; see Psalm 7:17.