Today, let us prove that the land promise was fulfilled for physical Israel; that is, the land of Canaan--to the fullest extent of God's promise--was possessed by Abraham's descendants.
There are several ways to confirm this truth. First, consider what I Kings 4:21 states - "So Solomon reigned over all kingdoms from the River to the land of the Philistines, as far as the border of Egypt. They brought tribute and served Solomon all the days of his life." This shows the far-reaching extent of the kingdom of Israel in Solomon's day. This most certainly fulfills what God declared to the patriarch Abraham in Genesis 15:18 - "To your descendants I have given this land, from the river of Egypt to the great river, the River Euphrates."
An explicit proof of the fulfilled promise is found in Nehemiah 9:7,8, where the people affirmed - "You are the LORD God, who chose Abram, and brought him out of Ur of the Chaldeans, and gave him the name Abraham; you found his heart faithful before You, and made a covenant with him to give the land of the Canaanites, the Hittites, the Amorites, the Perizzites, the Jebusites, and the Girgashites--to give it to his descendants. You have performed Your words, for You are righteous." God had performed His words pertaining to the land promise; He had fulfilled His oath to the patriarch.
A third proof of the fulfillment of the land promise can be seen through a careful study of the cities of refuge, which were required under the Mosaic covenant. It is learned from Deuteronomy 19:1-10 that there would only be three cities of refuge in Israel unless God fulfilled all of the land promise. If all of the land promised was actually given to the nation, then three more cities of refuge would be added for a total of six. The fact of the matter is that Joshua ultimately established six cities of refuge (Josh. 20:7-9). Therefore, it must be the case that God gave the children of Israel all the land He promised them via Abraham.
Joshua 21:43-45 also teaches - "The LORD gave to Israel all the land which He had sworn to give to their fathers, and they took possession of it and dwelt in it. The LORD gave them rest all around, according to all that He had sworn to their fathers. And not a man of all their enemies stood against them; the LORD delivered all their enemies into their hand. Not a word failed of any good thing which the LORD had spoken to the house of Israel. All came to pass" (cf. 23:14). It doesn't get much clearer than that.
However, let it be understood that this promise--like most of God's promises--was conditional (cf. Jer. 18:5-10). God told the people repeatedly that if they were faithful to Him, then He would continue to richly bless them. But, if they failed to carefully observe His commandments and statutes, He would bring many curses upon them (Deut. 28). The Israelites, through disobedience, could lose the land of Canaan that God had given them (Deut. 29:23-28; Lev. 20:22; I Kings 9:6,7). In fact, the people did lose the land because of their disobedience. II Chronicles 36:14-17 records - "Moreover all the leaders of the priests and the people transgressed more and more, according to all the abominations of the nations, and defiled the house of the LORD which He had consecrated to Jerusalem. And the LORD God of their fathers sent warnings to them by His messengers, rising up early and sending them, because He had compassion on His people and on His dwelling place. But they mocked the messengers of God, despised His words, and scoffed at His prophets, until the wrath of the LORD arose against His people, till there was no remedy. Therefore He brought against the them the king of the Chaldeans, who killed their young men with the sword in the house of their sanctuary, and had no compassion on young man or virgin, on the aged or the weak; He gave them all into his hand." The Hebrew people were later restored to the land (cf. Ezra and Nehemiah) before losing it again in A.D. 70.
Friends, God kept his promise to Abraham. He assured the patriarch that his descendants would inherit the land of Canaan, and that is exactly what happened. God is faithful; He keeps His word (Heb. 6:13-18). May we trust Him fully (i.e., without wavering), knowing that He will keep the assurances He has made to His people.