Thank you for the question on the genealogy of Jesus, “Did Jesus belong to the tribe of Judah?”
The genealogies given in the Gospels states that through the lineage of Joseph and Mary, Jesus is a descendant of Judah.
I. Joseph “adopted” Jesus as his own son.
Matthew 1 says this in the NASB-NIV Parallel New Testament in Greek and English, “(The) book of (the) generation of Jesus Christ, son of David son of Abraham…and Jacob begat Joseph the husband of Mary, of whom was born Jesus the (one) called Christ…Salmon was the father of Boaz by Rahab, Boaz was the father of Obed by Ruth, and Obed the father of Jesse. 6 Jesse was the father of David the king.…”.
Jesus is not born from his biological parent, Joseph since his conception was from God. God was his Father one might say. When Joseph married Mary, he adopted Jesus as his own son. Joseph’s lineage traces to the King David.
II. Mary is the mother of Jesus.
Luke 1 says this in the New American Standard Bible, “Now in the sixth month the angel Gabriel was sent from God to a city in Galilee called Nazareth, 27 to a virgin engaged to a man whose name was Joseph, of the descendants of David; and the virgin’s name was Mary.”
Luke 1 says this, “When He began His ministry, Jesus Himself was about thirty years of age, being, [h]as was supposed, the son of Joseph, the son of Eli, 24…31 the son of Melea, the son of Menna, the son of Mattatha, the son of Nathan, the son of David, 32 the son of Jesse, the son of Obed, the son of Boaz, the son of Salmon, the son of Nahshon,…(NASB). The lineage of Luke, in my opinion, is of Mary’s lineage since it is trace through Nathan
Luke 1 says this by the angel, “The angel said to her, “Do not be afraid, Mary; for you have found favor with God. 31 And behold, you will conceive in your womb and bear a son, and you shall name Him Jesus. 32 He will be great and will be called the Son of the Most High; and the Lord God will give Him the throne of His father David; 33 and He will reign over the house of Jacob forever, and His kingdom will have no end” (NASB).
If Jesus was not from the line of Judah, he could not inherit the throne of his father David nor rule over Israel. The angel declared that God will give him the throne of his father David. Thus Jesus qualified to be the son of David through Mary, his mother.
SUMMARY: Jesus is the “adopted” son of Joseph and biologically through Mary of whom both Joseph and Mary are from the lineage of David.
For more perspectives:
https://www.quora.com/Did-Jesus-belong-to-the-tribe-of-Judah