The Mitzvah to live in Eretz Yisroel is found in Bamidbar 33:53
וְהוֹרַשְׁתֶּ֥ם אֶת־הָאָ֖רֶץ וִֽישַׁבְתֶּם־בָּ֑הּ כִּ֥י לָכֶ֛ם נָתַ֥תִּי אֶת־הָאָ֖רֶץ לָרֶ֥שֶׁת אֹתָֽהּ׃
And you shall take possession of the land and settle in it, for I have assigned the land to you to possess.
The Ramban on that passuk states that it is a mitzvahs asei m'doraysa to settle in Eretz Yisroel. He mentions that Rashi seems to disagree with him, and as mentioned in the comments, so does the Rambam.
However the Pasuk in Bamidbar 33:51 states
דַּבֵּר֙ אֶל־בְּנֵ֣י יִשְׂרָאֵ֔ל וְאָמַרְתָּ֖ אֲלֵהֶ֑ם כִּ֥י אַתֶּ֛ם עֹבְרִ֥ים אֶת־הַיַּרְדֵּ֖ן אֶל־אֶ֥רֶץ כְּנָֽעַן׃
Speak to the Israelite people and say to them: When you cross the Jordan into the land of Canaan,
This seems to indicate that the mitzvah only begins AFTER they cross the Jordan River. Therefore, those who stayed behind were perhaps never included in the mitzvah. Once they conquered Eretz Yisroel, it could be, that Ever Hayarden was included as part of the mitzvah, as evident in the fact that a husband can't force his wife to move from Ever Hayarden to Eretz Yisroel.
In fact, the Netziv in Haamak Davar on this passuk, (Bamidbar 33:51) says something along these lines.
כי אתם עוברים את הירדן וגו׳. אבל כ״ז שלא עברו את הירדן לא״י לא הוזהרו להאביד ע״ז בעה״י. דאזהרה זו היא משום קדושת הארץ. ואין עה״י מתקדש אלא אחר שנתקדש א״י כמו לענין ערי מקלט שאינן קולטות עד שיהיו נגמר גם בא״י משום דערי מקלט תלוי בקדושת הארץ בזמן שהיובל נוהג. ויובל תלוי בזמן שכל ישראל על אדמתם וע׳ להלן ל״ה י׳ ומש״ה לא הוזהרו לבער ע״ז מעה״י עד שיטהרו מא״י:
When you cross. As long as they had not yet crossed the Yardein into Eretz Yisroel, they were not ordered to destroy the idol worship on the other side of the Yardein. This commandment depended on the holiness of the Land of Israel; the other side of the Yardein did not become sanctified until Eretz Yisroel was sanctified. This is similar to the concept of the Cities of Refuge that did not take in accidental murderers until those in Eretz Yisroel would also be sanctified, because the activation of the Cities of Refuge depends on the holiness of Eretz Yisroel which in turn is only when the Jubilee year is being observed.
This would also answer why, as mentioned in the comments, the Pesukim seem to say that Ever Hayarden was not counted as Eretz Yisroel while Moshe was alive, but today (or anytime after kivush haaretz) it is considered to have some kind of status of kedushas Haaretz.