He is the Lord our God - His name is Yahweh - the true God; and this God is ours. See the notes at Psalm 95:7.
His judgments are in all the earth - More properly "in all the land;" that is, in every part of the land he is honored as our God. His institutions are established here; his laws are obeyed here; his worship is celebrated here. No other God is worshipped here; everywhere he is acknowledged as the nation's God.

He is the Lord our God - He is Jehovah, the self-existent and eternal God. He is our God, he is our portion; has taken us for his people, and makes us happy in his love.
The following abstract of the history of the Israelites presents but few difficulties. See the notes on Psalm 78 (note).

He is the lord our God,.... Here begin the arguments to excite to praise and thankfulness; and the first is taken from what God is, and is to us; he is Jehovah, the Being of beings, a self-existent Being, the author of all beings, but receives his own from none; being undivided, independent, and self-sufficient, invariably and unchangeably the same, which is, and was, and is to come; and who has a sovereign power and authority over all creatures, whose name alone is Jehovah; nor is that name applicable or communicable to any created being; and yet this Jehovah is our God, our God in covenant, our God in Christ; our God that has blessed us with all spiritual blessings in Christ; our God that has regenerated, adopted, and justified us; that supplies all our wants, and will be our God and our portion for ever; and therefore worthy of all praise, honour, and glory.
His judgments are all the earth: not his laws and statutes, his word and ordinances, or the revelation of his mind and will as faith and worship, which are sometimes meant by his judgments; for these were not in all the earth, were only known to the people of the Jews at this time, Psalm 147:19, rather his judgments on the Egyptians, or his plagues upon them for refusing to let Israel go, the fame of which was spread throughout the world: and may take in all the judgments of God in other parts of the world, as on Sodom and Gomorrah, and especially the universal deluge, which destroyed the world of the ungodly; and by such judgments the Lord is known, Psalm 9:16 and for these he is to be praised; as they are expressive of his holiness and justice; as he will be for his judgments on antichrist, when they are made manifest, Revelation 15:4. This may also respect in general God's government of the world, and his righteous judging in it; who is a God that judgeth in the earth, and governs it by his power and wisdom, and in righteousness; and this righteous Judge is our God.

Rather, "He, Jehovah, is our God." His title, "JEHOVAH," implies that He, the unchangeable, self-existing Being, makes things to be, that is, fulfils His promises, and therefore will not forsake His people. Though specially of His people, He is God over all.

The poet now begins himself to do that to which he encourages Israel. Jahve is Israel's God: His righteous rule extends over the whole earth, whilst His people experience His inviolable faithfulness to His covenant. יהוה in Psalm 105:7 is in apposition to הוּא, for the God who bears this name is as a matter of course the object of the song of praise. זכר is the perfect of practically pledges certainty (cf. Psalm 111:5, where we find instead the future of confident prospect). The chronicler has זכרוּ instead (lxx again something different: μνημονεύωμεν); but the object is not the demanding but the promissory side of the covenant, so that consequently it is not Israel's remembering but God's that is spoken of. He remembers His covenant in all time to come, so that exile and want of independence as a state are only temporary, exceptional conditions. צוּה has its radical signification here, to establish, institute, Psalm 111:9. לאלף דּור (in which expression דור is a specifying accusative) is taken from Deuteronomy 7:9. And since דּבר is the covenant word of promise, it can be continued אשׁר כּרת; and Haggai 2:5 (vid., Khler thereon) shows that אשׁר is not joined to בריתו over Psalm 105:8. וּשׁבוּעתו, however, is a second object to זכר (since דּבר with what belongs to it as an apposition is out of the question). It is the oath on Moriah (Genesis 22:16) that is meant, which applied to Abraham and his seed. לישׂחק (chronicler ליצחק), as in Amos 7:9; Jeremiah 33:26. To זכר is appended ויּעמרדה; the suffix, intended as neuter, points to what follows, viz., this, that Canaan shall be Israel's hereditary land. From Abraham and Isaac we come to Jacob-Israel, who as being the father of the twelve is the twelve-tribe nation itself that is coming into existence; hence the plural can alternate with the singular in Psalm 105:11. את־ארץ כּנען (chronicler, without the את) is an accusative of the object, and חבל נחלתכם accusative of the predicate: the land of Canaan as the province of your own hereditary possession measured out with a measuring line (Psalm 78:55).

Judgments - God executes his judgments upon all nations and people.