Genesis 9:8–11 (ESV)

8 Then God said to Noah and to his sons with him,

We now read for the second time in this chapter that the Lord speaks directly to Noah and his sons. The Lord establishes his covenant with them and with all creation.

This is not about a new covenant that did not actually exist as yet. This covenant is a confirmation, and, in a sense, it serves as an extension of the covenant that already existed between God and man in paradise. The Hebrew word translated here as establish does not always indicate a new situation. The word can also mean to confirm or to fulfill. Other examples are Deuteronomy 8:18; Deuteronomy 9:5; 1 Samuel 1:23; 1 Samuel 3:12; 1 Kings 2:4; Jeremiah 29:10; Jeremiah 33:14.

The special meaning of the covenant words of the Lord here is that he promises to the whole creation that a worldwide flood will never again destroy it. By his faithfulness to his covenant, the Lord shows that he looks upon his creation with love and mercy, and that he will act in this way. The Lord also has a heart for the animals (see e.g., Jonah 4:11.)