Let’s read verses 8-9, “But to the Son He says: ‘Your throne, O God, is forever; a scepter or righteousness is the scepter of Your kingdom. You have loved righteousness and hated lawlessness; Therefore God, Your God, has anointed You with the oil of gladness more than Your companions.” The words, “But to the Son He says” makes it clear that God the Father is speaking to His eternal Son, who is also God. How we know that the Son is also God? Because the first thing the Father says to Him is, “Your throne, O God, is forever and ever.” The Father calls Him God BECAUSE HE IS GOD! Scripture confirms that truth in many passages. Here is one of them: “In the beginning was the Word, and the Word was with God, and the Word was God…And the Word became flesh and dwelt among us, and we beheld His glory, the glory as of the only begotten of the Father, full of grace and truth…No one has seen God at any time. The only begotten SON, who is in the bosom of the Father, He has declared Him” (John 1:1, 14, 18). In verse 1 we learn that the Son of God (who is also called “the Word”) was not only “with God,” but that He “was God.” This does NOT mean that “God also has a God”; it means that God is made up of more than One Person. The fact is God is a Triune God made up of Three Persons; the Father, the Son, and the Holy Spirit (see Matthew 28:19). Each Person is coequal and share the same attributes of being Omnipotent (all-powerful), Omniscient (all-knowing), and Omnipresent (present everywhere at the same time).

We saw in verse 14 above that “the Word became flesh and dwelt among us.” This is the truth of the Incarnation of the Son of God. He became a true human being. Before He was born into the human race an angel appeared to a virgin named Mary to announce to her that she would His mother (see Luke 1:26-35). In verses 31-33 we read, “And behold, you will conceive in your womb and bring forth a Son, and shall CALL His name JESUS. He will be great, and will be called the Son of the Highest; and the Lord God will give Him the throne of His father David.” Mary asked “How can this be, since I do not know a man” (verse 34)? The angel then told her, “The Holy Spirit will come upon you, and the power of the Highest will overshadow you; therefore, also that Holy One who is to be born will be CALLED the Son of God” (verse 35). Notice, He would be called “Jesus” and He would be called “the Son of God.” Why? Ah, because He would be a true human being and He would still be God. We saw in verse 18 He came to “declare the Father”; that is, to manifest God to the world. He was “God manifested in the flesh” (see 1st Timothy 3:16).

I have quoted those verses (in John 1 and Luke 1) in order to answer your question of why God the Father could say to Him, “Therefore God, Your God.” Because the eternal Son became a true Man, He walked on this earth in submission to God as a true Servant who would lay down His life to provide salvation for lost sinners (see Philippians 2:5-8). This means that He, as a Man, walked in dependence upon God (just as all men should be walking in obedience to God). He even called Him “My God” as the Perfect Man in Matthew 27:46; John 20:17; and Revelation 3:12. God the Father acknowledged His perfect life of obedience and holiness and would reward Him for it. This is seen in the Father’s words to Him, “You have loved righteousness and hated lawlessness; Therefore God, Your God, has anointed You with the oil of gladness more than Your companions.” This means that because Jesus walked in perfect holiness (loving righteousness and hating lawlessness) every minute of every day on earth, God would exalt Him above all other human beings. We read of this in Philippians 2:9-11, “Therefore God also has highly exalted Him and given Him the name above every name, that at the name of Jesus every knee should bow, of those in heaven, and of those on earth, and of those under the earth, and that every tongue should confess that Jesus Christ is Lord, to the glory of God the Father.”  (DO)  (524.3)