“Who of our father through the Holy Spirit, of the mouth of David your servant, said, ‘Why did the Gentiles rage, And the peoples imagine vain things? The kings of the earth set themselves in array, And the rulers were gathered together, Against the Lord, and against his Anointed.' ”
Then they recalled what the Holy Spirit had spoken through David in Psalms 2 (cited from LXX). Note their confidence in the fact that the Psalms are the words of the Holy Spirit. In the Psalm God's challenge had gone out to all who opposed God's people. They raged, they imagined vain things, they set themselves in array, they mobilised. But it was all in vain, for it was against the Lord and against His Anointed, and therefore they could not win. And the Psalm goes on to point out that all such opponents will be defeated when the Lord's Anointed achieves His triumph. It was from this Psalm that the words spoken at Jesus baptism were taken ‘You are My Son --'. Thus they saw it as quite clear from the Psalm that all the raging against the Name of Jesus would come to nothing. Jesus was God's Anointed, and nothing could therefore stand in the way of His victory.
The Messiah is elsewhere described as the Lord's Anointed in Psalm of Solomon Acts 7:26, while reference to Psalms 2 as Messianic appears at Qumran. So the connection of Psalms 2 and the title ‘the Lord's Anointed' with the Messiah was already established.
The idea here may be that Jesus was anointed with the Spirit at His baptism when the Holy Spirit came on Him like a dove (Luke 3:22 compare Acts 10:38), something further validated at the Transfiguration (Luke 9:29; Luke 9:35). Or it may simply indicate that He was seen as such because He was ‘the Son' Who was sent from God and was full of the Holy Spirit (Luke 4:1). Either way He was the Chosen One of God.
The Greek of Acts 4:25 which we have sought to render literally is difficult, but as Luke presumably takes it from his source and does not alter it he clearly saw it as acceptable Greek.