The Ramban (Rav Moshe Nahmanides, Spain, 1194-1270), commenting on the verse, "You shall possess the land and reside in it" (Bamidbar 33:53), understood that the Torah here introduces an affirmative command to live in the Land of Israel. In the Ramban’s view, this command is relevant even after the destruction of the Bet Ha’mikdash. The Ramban articulates this position also in his critique of the listing of the 613 Misvot by the Rambam (Rav Moshe Maimonides, Spain-Egypt, 1135-1204). He objects to the Rambam’s omission of this Misva from his list, insisting that living in the Land of Israel is among the 613 Biblical commands.
The Megilat Ester commentary to the Rambam’s Sefer Ha’misvot (by Rav Yishak de Leon, 15th century) understood that the Rambam does not list living in Israel as a Biblical command because he felt that there is no obligation to live there after the destruction of the Bet Ha’mikdash. Once we were driven into exile, we are to remain in exile until Mashiah arrives and brings us back to our homeland.
Many others, however, disagreed with the Megilat Ester’s understanding of the Rambam’s position. Hacham Ovada Yosef, in Yabia Omer (vol. 11), brings a number of proofs showing that even the Rambam maintained that there is a Misva to reside in the Land of Israel nowadays. For example, the Rambam brings the Halacha mentioned in the Talmud that if a husband wishes to move to Israel and his wife refuses, her refusal is legal grounds for divorce, and the husband may then divorce her without paying the Ketuba. Quite obviously, this Halacha is predicated on the fact that moving to Israel is a Misva; after all, if the husband wanted to move anywhere else, this Halacha does not apply. The fact that the Rambam codifies this Halacha, without mentioning that it applies only during the time of the Bet Ha’mikdash, clearly demonstrates that he acknowledged a Misva to live in Eretz Yisrael even nowadays.
The Rambam also codifies the extraordinary provision allowing one who is purchasing property in Eretz Yisrael to ask a gentile to draw up the contract on Shabbat, if this is necessary to finalize the transaction. Normally, of course, it is forbidden to ask a gentile to perform an act on Shabbat that is forbidden for Jews. And even for the sake of a Misva, it is permissible to ask a gentile only to perform an action that is forbidden for Jews on the level of Rabbinic enactment, but not an action forbidden on the level of Torah law. Nevertheless, due to the importance of Yishub Eretz Yisrael (settling the Land of Israel), the Sages permitted asking a gentile to write a contract on Shabbat if this is necessary to finalize the purchase of a property in the Land of Israel. The Rambam’s codification of this law would certainly indicate that he maintained that Yishub Eretz Yisrael constitutes a Misva.
Yet a third proof is the Rambam’s ruling that one who moves into a home in the Land of Israel must affix Mezuzot immediately. Outside the Land of Israel, one must affix Mezuzot within thirty days of moving into a home, because before thirty days, he is considered as though he resides in the home temporarily. In the Land of Israel, however, one’s residence is immediately considered permanent. This, too, seems to prove that living in Israel constitutes a Misva even nowadays, and even according to the Rambam.
The Tashbetz (Rav Shimon Ben Semah Duran, Algiers, 1361-1444), like the Ramban, writes explicitly that living in Israel is a Misva even nowadays.
Tosafot in Masechet Ketubot (110) cite Rabbenu Haim as stating that there is no Misva whatsoever to live in the Land of Israel nowadays. However, a number of later Rishonim (including the Hagahot Mordechi) questioned whether Rabbenu Haim actually made such a statement, as this may have actually said by a student, and was misattributed. Others, including the Meshech Hochma (Rav Meir Simcha Ha’kohen of Dvinsk, Lithuania, 1843-1926), noted that from Rabbenu Haim’s formulation, it appears that he meant there is no Misva to live in Eretz Yisrael if one will not ensure to observe all the Misvot. While the Misvot are, of course, binding everywhere, the Land of Israel is "the palace of the King," and so violating G-d’s will in the Land of Israel, His "palace," is especially egregious. However, if one is committed to observing the Misvot, then even Rabbenu Haim will agree that there is a Misva to live in Eretz Yisrael.
The Arizal (Rav Yishak Luria, 1534-1572) wrote that those who live in Eretz Yisrael experience a special spiritual elevation, raising their souls from the level of "Nefesh" to the high level of "Neshama." This is in contrast to those who simply visit the land, whose souls are elevated only to the level of "Ru’ah." The Arizal explains on this basis the verse in the Book of Yeshayahu (42:5), "Noten Neshama La’am Aleha Ve’ru’ah La’holechim Bah" – G-d grants the level of "Neshama" to those who reside in the land ("La’am Aleha"), and He grants the level of "Ru’ah" to those who visit temporarily ("La’holechim Bah").
As for the final Halacha, Rav Moshe Feinstein (Russia-New York, 1895-1986) maintained that although, as the aforementioned sources indicate, living in Eretz Yisrael is a Misva, at last according to most opinions, nevertheless, it is not obligatory. In Rav Feinstein’s view, one who lives in Eretz Yisrael fulfills a Misva, but there is no obligation to do so. Rav Feinstein proves this conclusion from the fact that the Rambam never writes explicitly that one may not live outside the Land of Israel.
Hacham Ovadia, however, disagrees, and states emphatically that there is an obligation to live in Eretz Yisrael nowadays. He adds that although one is able to devote oneself to Torah learning and Misva observance outside the land, nevertheless, there is a Misva to move to the Land of Israel.
Summary: Different opinions exist as to whether there is a Misva to live in the Land of Israel nowadays. Some maintained that living there fulfills a Misva, but this is not obligatory. Hacham Ovadia Yosef, however, felt that there is an outright obligation to live in Eretz Yisrael.