What is the reason to rejoice?
'Rashi': When a person becomes king, everyone is sad, for they do not know how he will be. When Hashem will reign, Shamayim and Aretz will rejoice, and all the straight will say 'now Hashem reigned; He returned the Aron to us.'
Radak (Tehilim 96:11): This and the coming verse are metaphors for the great Simchah that there will be due to the great Shalom and good that will be in the world. Regarding the opposite of Shalom, metaphors say "Shemesh v'Yare'ach Kadaru" (Yo'el 2:10), "Avlah Navlah ha'Aretz" (Yeshayah 24:4
Why does it mention Simchah regarding Shamayim, and Gil regarding the land?
Vilna Gaon: Simchah is only for something new; Gil is even for something old. Only Gil applies to the land, for "v'Ein Kol Chadash Tachas ha'Shamesh" (Koheles 1:9), but there is Chidush above the sun in Shamayim, so there is Simchah there 1 .
Malbim (Tehilim 96:11): Simchah is constant joy. Gil is something that comes new. It is proper to have Simchah over the fixed conduct, and Gil over something unusual. Shamayim always acts according to natural orders; it always has Simchah. When reward comes to the land not according to the normal order, Gil applies. Both of them can be together. Shamayim and the Ma'arachah go according to their nature, and the land is conducted according to Hashgachah and recompense for deeds. This can be in two ways; refer to Tehilim 96:11:3:2, 96:12:2:1.
Hagahah from the Vilna Gaon's grandson: Also this is a mistake; the Vilna Gaon never said so.
Why does it say "Hashem Malach" (past tense)?
Rashi (Tehilim 96:10): They will sing so in the future (Hashem already became king).
Radak (Tehilim 96:10): They will recognize His kingship, for He took His nation out of Galus with great honor. Even their [former] rulers took them to their land! They will see that He rules over everything, and kingship is His. They will recognize the Mishpat that He did to the Goyim who came against Yerushalayim.
Malbim (Tehilim 96:10): They will recognize that also natural conduct is totally hidden miracles. He arranged nature so that also Mishpat will be found for reward and punishment. Nature does not conduct the world alone; refer to 16:30:3:2.
