When Samuel comes to anoint the new king, Jesse presents his sons and David is the youngest, making clear that Jesse is David's father and that David comes from Jesse's household in Bethlehem.
וַיֹּ֨אמֶר יְהֹוָ֜ה אֶל־שְׁמוּאֵ֗ל עַד־מָתַי֙ אַתָּה֙ מִתְאַבֵּ֣ל אֶל־שָׁא֔וּל וַאֲנִ֣י מְאַסְתִּ֔יו מִמְּלֹ֖ךְ עַל־יִשְׂרָאֵ֑ל מַלֵּ֨א קַרְנְךָ֜ שֶׁ֗מֶן וְלֵ֤ךְ אֶֽשְׁלָחֲךָ֙ אֶל־יִשַׁ֣י בֵּֽית־הַלַּחְמִ֔י כִּֽי־רָאִ֧יתִי בְּבָנָ֛יו לִ֖י מֶֽלֶךְ׃ וַיֹּ֨אמֶר שְׁמוּאֵ֣ל אֶל־יִשַׁי֮ הֲתַ֣מּוּ הַנְּעָרִים֒ וַיֹּ֗אמֶר ע֚וֹד שָׁאַ֣ר הַקָּטָ֔ן וְהִנֵּ֥ה רֹעֶ֖ה בַּצֹּ֑אן וַיֹּ֨אמֶר שְׁמוּאֵ֤ל אֶל־יִשַׁי֙ שִׁלְחָ֣ה וְקָחֶ֔נּוּ כִּ֥י לֹֽא־נָסֹ֖ב עַד־בֹּא֥וֹ פֹֽה׃ וַיִּשְׁלַ֤ח וַיְבִיאֵ֙הוּ֙ וְה֣וּא אַדְמוֹנִ֔י עִם־יְפֵ֥ה עֵינַ֖יִם וְט֣וֹב רֹ֑אִי {פ} וַיֹּ֧אמֶר יְהֹוָ֛ה ק֥וּם מְשָׁחֵ֖הוּ כִּי־זֶ֥ה הֽוּא׃
And GOD said to Samuel, “How long will you grieve over Saul, since I have rejected him as king over Israel? Fill your horn with oil and set out; I am sending you to Jesse the Bethlehemite, for I have decided on one of his sons to be king.” Then Samuel asked Jesse, “Are these all the boys you have?” He replied, “There is still the youngest; he is tending the flock.” And Samuel said to Jesse, “Send someone to bring him, for we will not sit down to eat until he gets here.” So they sent and brought him. He was ruddy-cheeked, bright-eyed, and handsome. And GOD said, “Rise and anoint him, for this is the one.”