Then Moses gave to the Gadites, the Reubenites and the half-tribe of Manasseh son of Joseph the kingdom of Sihon king of the Amorites and the kingdom of Og king of Bashan--the whole land with its cities and the territory around them.
The promised land included the territory east of the Jordan. Moses took that land and gave it to Isreal.
Moses didn't die in the wilderness.
Deuteronomy 34:1 Then Moses climbed Mount Nebo from the plains of Moab to the top of Pisgah, across from Jericho. There the Lord showed him the whole land—from Gilead to Dan, 2all of Naphtali, the territory of Ephraim and Manasseh, all the land of Judah as far as the Mediterranean Sea, 3the Negev and the whole region from the Valley of Jericho, the City of Palms, as far as Zoar. 4Then the Lord said to him, “This is the land I promised on oath to Abraham, Isaac and Jacob when I said, ‘I will give it to your descendants.’ I have let you see it with your eyes, but you will not cross over into it.”
5And Moses the servant of the Lord died there in Moab, as the Lord had said. 6He buried him in Moab, in the valley opposite Beth Peor, but to this day no one knows where his grave is.
Even though Moses didn't cross the Jordan, he did his job. The rest of the conquest was carried on by Joshua.
Joshua 21:43 So the Lord gave Israel all the land he had sworn to give their ancestors, and they took possession of it and settled there. 44The Lord gave them rest on every side, just as he had sworn to their ancestors. Not one of their enemies withstood them; the Lord gave all their enemies into their hands. 45Not one of all the Lord’s good promises to Israel failed; every one was fulfilled.