And the Lord hath avouched - Publicly declared, by the blessings he pours down upon them, that he has taken them to be his peculiar people. Thus the covenant is made and ratified between God and his followers.

(o) And the LORD hath avouched thee this day to be his peculiar people, as he hath promised thee, and that [thou] shouldest keep all his commandments;
(o) Signifying that there is a mutual bond between God and his people.

And the Lord hath avouched thee this day to be his peculiar people,.... Affirmed and declared them to be his special people, above all people on the face of the earth, and that they were looked upon and considered by him as his jewels, his peculiar treasure:
as he hath promised thee; on condition of their obedience to him, as he did in Exodus 19:5,
and that thou shouldest keep all his commandments; at the same time declared this as his will, that they should observe all his precepts, to which they were laid under obligation by the special favour and peculiar privileges he bestowed upon them, Deuteronomy 7:6. The Targums interpret both these verses of the people of Israel choosing and making the Lord their King, and of his being made King over them; and so it respects their peculiar form of civil government, being a theocracy. The Lord's people in Christ are a peculiar people; they are distinct from all people, and are peculiarly regarded by him; they are the objects of his peculiar love, and receive peculiar favours from him; and whom having chosen and redeemed, he calls by his special grace, and witnesses their special relation to him by his Spirit; which grace obliges and excites them to a cheerful obedience to his commands.

Avouched thee - Hath owned thee for such before all the world by eminent and glorious manifestations of his power and favour, by a solemn entering into covenant with thee, and giving peculiar laws, promises, and privileges to thee above all mankind.