These Promises will be fulfilled in the establishment of the Kingdom of David under Christ (that is, in the setting up of the Kingdom of God on earth) as the centre of universal empire.

First - As to the blessing of all nations:

The earth shall be full of the knowledge of the LORD, as the waters cover the sea. (Isaiah 11:9).

And he shall judge among the nations, and shall rebuke many people: and they shall beat their swords into plowshares, and their spears into pruninghooks: nation shall not lift up sword against nation, neither shall they learn war any more. (Isaiah 2:4).

He shall judge the poor of the people, he shall save the children of the needy, and shall break in pieces the oppressor...His name shall endure for ever: his name shall be continued as long as the sun: and men shall be blessed in him: all nations shall call him blessed.(Psalm 72:4,17).

The nations shall bless themselves in him, and in him shall they glory. (Jeremiah 4:2).
And in that day there shall be a root of Jesse, which shall stand for an ensign of the people; to it shall the Gentiles seek: and his rest shall be glorious. (Isaiah 11:9-10).

Behold, a king shall reign in righteousness, and princes shall rule in judgment. And a man shall be as an hiding place from the wind, and a covert from the tempest; as rivers of water in a dry place, as the shadow of a great rock in a weary land. And the eyes of them that see shall not be dim, and the ears of them that hear shall hearken. The heart also of the rash shall understand knowledge, and the tongue of the stammerers shall be ready to speak plainly. (Isaiah 32:1-6; Jeremiah 3:17).

The battle bow shall be cut off: and he shall speak peace unto the heathen: and his dominion shall be from sea even to sea, and from the river even to the ends of the earth. (Zechariah 9:10).

The LORD is exalted...and wisdom and knowledge shall be the stability of thy times, and strength of salvation (Isaiah 33:5-6).

O let the nations be glad and sing for joy: for thou shalt judge the people righteously, and govern the nations upon earth. (Psalm 67:4).

Second - As to the inheritance of the Land of Promise:

Then will I remember my covenant with Jacob, and also my covenant with Isaac, and also my covenant with Abraham will I remember; and I will remember the land. (Leviticus 26:42).

Then will the LORD be jealous for his land, and pity his people... Fear not, O land; be glad and rejoice: for the LORD will do great things. (Joel 2:18,21).

A land which the LORD thy God careth for: the eyes of the LORD thy God are always upon it, from the beginning of the year even unto the end of the year. (Deuteronomy 11:12).

And the desolate land shall be tilled, whereas it lay desolate in the sight of all that passed by. And they shall say, This land that was desolate is become like the garden of Eden; and the waste and desolate and ruined cities are become fenced, and are inhabited. Then the heathen that are left round about you shall know that I the LORD build the ruined places, and plant that that was desolate: I the LORD have spoken it, and I will do it. (Ezekiel 36:34-36).

For the LORD shall comfort Zion: he will comfort all her waste places; and he will make her wilderness like Eden, and her desert like the garden of the LORD; joy and gladness shall be found therein, thanksgiving, and the voice of melody. (Isaiah 51:3).

Thou shalt no more be termed Forsaken; neither shall thy land any more be termed Desolate: but thou shalt be called Hephzibah, and thy land Beulah: for the LORD delighteth in thee, and thy land shall be married. (Isaiah 62:4).

Whereas thou hast been forsaken and hated, so that no man went through thee, I will make thee an eternal excellency, a joy of many generations. (Isaiah 60:15).

Ye shall see Abraham, and Isaac, and Jacob, and all the prophets, in the kingdom of God (Luke 13:28).

And I say unto you, That many shall come from the east and west, and shall sit down with Abraham, and Isaac, and Jacob, in the kingdom of heaven. (Matthew 8:11).

Thou wilt perform the truth to Jacob, and the mercy to Abraham, which thou hast sworn unto our fathers from the days of old. (Micah 7:20).

But as truly as I live, all the earth shall be filled with the glory of the LORD. (Numbers 14:21).