This Messianic prophecy is of Jesus coming to rule and reign over all the people of the world…both Jew and Gentile.  This is also shown in Isaiah 49:6 where it says that Jesus is coming not only to Israel, but to the Gentiles…”that You may bring My salvation to the ends of the earth.”  It’s not that there’d be a continuous reign by the descendants of Judah…only the promise of the permanent right to rule…this being in Jesus Christ, the Messiah.  And at that time He will say, ” Before Me every knee will bow; by Me every tongue will swear.”  (Isaiah 45:23)