The Old Testament is full of references of God reigning from Mount Zion on which Jerusalem sits (2 Samuel 5:7). There are references to the kingdom reign of the Messiah who rules from Zion. These are Messianic Psalms expressing the hope of the people that God will rule with them again:
Psalm 2:6 ("Yet I have set My King On My holy hill of Zion")
9:11 ("Sing praises to the LORD, who dwells in Zion!")
48:2 ("Is Mount Zion on the sides of the north, The city of the great King")
50:2 ("Out of Zion, the perfection of beauty, God will shine forth")
This is a brief listing of phrases containing "zion;" click here to read of more passages: https://www.blueletterbible.org/search/search.cfm?Criteria=zion&t=NKJV#s=s_primary_0_1
We can infer that Jesus is the one who will be the one reigning there by comparing passages in Zechariah and Acts. Zechariah 14:3-5 reports that the "LORD" will go and fight against the nations (presumably the nations led by the end-times' antichrist figure, which will surround Israel to wipe it out --see the near-and-far-fullfillment of Luke 21:20), and the LORD will stand on the Mount of Olives. Is the LORD the same as the Lord Jesus Christ?
Then in Acts 1:9-11, two men appear before the disciples when Jesus rose up from the Mount of Olives and tell them that He will return the same way He left. Presumably this means He will return to the same place. This links Him to the "LORD" of the previous paragraph, and therefore to the LORD who will reign in Mt. Zion on earth. Revelation 20:6 says that they "will reign with Him a thousand years," so the Lord Jesus stays on earth during that time.
This brief study seems to indicate that the Lord Jesus will indeed physically reign from Zion at Jerusalem. Some theorize that the city of God in Revelation 21:1-2 comes down to earth and intersects with Zion so the Lord reigns in both earthly and heavenly spheres (sorry, I can't immediate recall the source of this idea).