The Gemara in Masechet Shabbat (41) cites the view of Rav Yehuda that it is forbidden to leave Babylonia to live in Eretz Yisrael. Rav Yehuda based his ruling on a verse in the Book of Yirmiyahu (27:22), "Babela Yuba’u Ve’shama Yiheyu" – "They shall be brought to Babylonia, and there they shall be." The Gemara notes that Rav Yehuda felt so strongly about this prohibition that his student, Rabbi Zera, who wanted to go live in Eretz Yisrael, avoided his Rabbi in order not to come under criticism for this aspiration.
It is clear that Halacha does not follow Rav Yehuda’s opinion. We know of many Amor’aim (Rabbis from Talmudic times) who moved from Babylonia to Eretz Yisrael, including Rabbi Zera, as well as many Rishonim (Medieval scholars) and Aharonim (scholars after the Shulhan Aruch) who moved to and settled in Eretz Yisrael. Indeed, stories abound of great sages who embarked on long voyages and trips in order to move to Eretz Yisrael, demonstrating that Halacha certainly allows settling in the Land of Israel. And, in fact, it is even considered a Misva to settle in Eretz Yisrael.
The Meiri (Rabbi Menahem Meiri, France, 13th century), in his commentary to Masechet Ketubot, explains that Rav Yehuda’s view is based upon the stature of Babylonia at that time as a major Torah center, a place where Torah scholarship and observance flourished. Rav Yehuda forbade leaving Babylonia because this meant moving to an area with a lower standard of Torah life, thus compromising one’s level of Torah and Yir’at Shamayim (fear of Heaven). But it is certainly permissible to live in a place with a high standard of Torah learning and observance, whether this is in Israel or in the Diaspora. Eretz Yisrael has certainly served as a major center of Torah, and even in the Diaspora, there are, of course, many areas, especially in the United States, where one can maintain a proper standard of religious life. Needless to say, one cannot compare the Torah of the United States with the Torah of Eretz Yisrael; as the Sages famously taught, "En Torah Ke’Torat Eretz Yisrael" – "There is no Torah like the Torah of the Land of Israel." Nevertheless, it is certainly acceptable to live in areas in the Diaspora with thriving Torah institutions and communities, and it is certainly permissible – and even a Misva – to leave such an area to live in Eretz Yisrael.
