Jesus is the prophesied Messiah
From the texts and their contexts cited in connection with Jesus being anointed with the Holy Spirit, the Bible student can taught how they teach that He is the Messiah.
John 3:34. "For he whom God hath sent speaketh the words of God: for God giveth not the Spirit by measure unto him."
This is a part of the Baptist's testimony concerning Jesus. In simple and incisive language he points out the criteria for Jesus being the heavenly-sent One, who is above all. The Father, in equipping the Son to be the promised deliverer, furnished him with power and all sustenance, as predicted in the Servant Songs of Isaiah (for instance, 42:1-4), not least of being the recipient of the Spirit: "Behold my servant, whom I have chosen; my beloved, in whom my soul is well pleased: I will put my spirit upon him, and he shall shew judgement to the Gentiles." Thus John incontrovertibly proves that Jesus is the long-expected Messiah.
Psalm 45:7. "Thou lovest righteousness, and hatest wickedness: therefore God, thy God, hath anointed thee with the oil of gladness above thy fellows."
The king is addressed as God in verse 6 of the same Psalm, and is distinguished from God in this verse. Verse 6 was likely a royal hyperbole (extravagant exaggeration) of the king referred to (perhaps Solomon), but ultimately refers to Jesus as the Christ, as is proven from Hebrews 1:8,9.
Jesus' basic qualification for Messiahship is the fact that he is sinless, unblameable, spotless and perfect in every respect. As God's representative and the restorer of his people, he holds a sceptre of rectitude and holiness.
Being God and man in one person, he is entrusted with the mission of accomplishing salvation, and his success is ensured. Though he had to suffer, it is with the oil of gladness that he is anointed. This same king, here prophesied, for the joy set before him, endured the cross, despising its shame and is now set at the right hand of the majesty on high (Hebrews 12:2).
Hebrews 1:9. "Thou hast loved righteousness, and hated iniquity; therefore God, even thy God, hath anointed thee with the oil of gladness above thy fellows."
The author here quotes a series of texts from the Old Testament to prove that Jesus is superior to the prophets and even the angels, for the simple fact that he is a divine person. As God's Son he speaks for God, maintains and governs the universe and, most significantly, has purged our sins (Hebrews 1:1-3).
In this particular quote, we know that historically the psalm was probably sung at a Hebrew monarch's wedding. What was true of the ancient king by virtue of his office, the writer to the Hebrews sees to be wholly true of Christ by virtue of His nature.
The Messiah was to be a divine person, and that is exactly what the context shows Jesus to be, being addressed by the Father in this way: "Thy throne, O God, is for ever and ever." And certainly the Messiah was sent to establish God's rule in and over the hearts of men.
Matthew 3:16. "And Jesus, when he was baptised, went up straightway out of the water: and lo, the heavens were opened unto him, and he saw the Spirit of God descending like a dove, and lighting upon him."
Here we find the first clear expression of the blessed truth concerning the Triune God in the whole New Testament. The descent of the Spirit upon Jesus was for special power at the beginning of his public ministry, in which he was to be the Prophet, speaking the words of God, the Great High Priest, making atonement and interceding for his people, and as King, ruling and defending the same.
John the Baptist also witness the Spirit's descent upon Jesus, as we read in John 1:32,33: "And John bare record, saying, I saw the Spirit descending from heaven like a dove, and it abode upon him. And I knew him not, but he that sent me to baptize with water, the same said unto me, Upon whom thou shalt see the Spirit descending, and remaining upon him, the same is he which baptizeth with the Holy Ghost."
The Father's testimony from above (which, Jesus maintained, was sufficient) and John's testimony from below (given "that ye might believe") both confirm Jesus' identification as the Servant of the Lord (Isaiah 42:1; cf. Exodus 4:22) and connects this with the messianic kingship (Psalms 2:7).
Luke 4:1,14,18. "And Jesus being full of the Holy Ghost returned from Jordan, and was led by the Spirit into the wilderness...And Jesus returned in the power of the Spirit into Galilee, and there went out a fame of him through all the region round about....The Spirit of the Lord is upon me, because he hath anointed me to preach the gospel to the poor; he hath sent me to heal the brokenhearted, to preach deliverance to the captives, and recovering of sight to the blind, to set at liberty them that are bruised..."
The temptation, who preceded his public ministry, was in the plan of God. Right at the beginning, Jesus faced the question of what sort of Messiah He was to be. The trails he faced with Satan was not to see whether he would sin or not (for he could not sin, though the pressures of temptation were real and forceful), but to prove him conqueror over sin and Satan.
The fact that Jesus was led constantly by the Spirit indicates that He is indeed the Messiah, as was foretold in Isaiah 11:2: "The Spirit of the Lord shall rest upon Him, the Spirit of wisdom and understanding, the Spirit of counsel and might, the Spirit of knowledge and of the fear of the Lord."
As he entered the synagogue of Capernaum, and stood up to read Isaiah, the portion he selected (Isaiah 61:1-2) was fulfilled in the hearing of his audience. In other words, He was the fulfilment of these words: "The Spirit of the Lord God is upon Me because the Lord has anointed Me," which verb, anointed, indicated the Messiah.