The impetus for this post was brought about through numerous conversations with a Lubavitch friend of mine. It occurred to me that the halachic underpinnings for Rav Kooks thought as well as those of his followers were not clearly known among the broader Orthodox community. This post and the upcoming ones will hopefully dispel some myths, as well as promote some serious discussion and debate.
If there is one passage that in my opinion sums up the thought of the followers of Rav Kook, it is this passage from the Ramban. The Ramban in his commentary to the Rambam’s "Sefer Hamitzvot" (Positive Commandment #4) notes the following.
"That we are commanded to take possession of the Land which the Almighty, Blessed Be He, gave to our forefathers, to Avraham, to Yitzhak, and to Yaacov; and not to abandon it to other nations, or to leave it desolate, as He said to them, You shall dispossess the inhabitants of the Land and dwell in it, for I have given the Land to you to posses it, (Numbers, 33:53) and he said, further, To Inherit the Land which I swore to your forefathers, (to give them,) behold, we are commanded with the conquest of the land in every generation."
(Footnote 48, Pg 112, "Torat Eretz Yisrael", David Samson)
Rav Tzvi Yehuda Kook extrapolates upon this Ramban:
"People occasionally ask, ‘Where is it written in the Torah we have to build a State?’ Aren’t they familiar with the words of the Ramban, who determines that we are commanded that this Land be in our hands, and not in the hands of any other nation? That it be in our hands in a national sense. Everyone understands that dominion over a geographic section of land demands political sovereignty and government. All of the Poskim (arbitrators of Torah law) both Rishonim and Achronim  , decide the law in this fashion, on the basis of this Ramban, that the precept of conquering the Land applies in all generations – and all of them agree it is a commandment of the Torah."
(Page 166, "Torat Eretz Yisrael", David Samson)
 See Pitchei Teshuva, Even HaEzer, Section 75, Sub-section 6.
 The following is a partial listing of the Halachic authorities who state that the obligation to live in Israel is a Torah commandment binding in all times (Footnote 51, Pg 113, "Torat Eretz Yisrael", David Samson):
Rambam Laws of Marriage Ch 3:20
Rambam Laws of Slaves Ch 8:39
Sefer Haredim Ch 7
Maharit Responsa 2:28
Knesset Gedolah Even HaEzer 75, Notes To the Beit Yosef 25
Gaon of Vilna Yoreh Deah 267:161
Avne Nezer Yoreh Deah 454
M’il Tzedakah Responsa 26
Rav Yaakov Emden, Mor Uktziah Section 1 Pg 16
Chida Responsa Yosef Ometz 52
Chida Ya’ir Ozen 10:15
Chachmat Adam, Shar Mishpatei HaAretz 11:13
Paat HaShulchan Ch1, Beit Yisrael 14
Chatam Sofer Responsa Yoreh Deah 233, 235
Rav Haim Palagi, Responsa Nishmat Kol Chai, Yoreh Deah 48
Rav Shlomo from Lublin, in his introduction to the book Mitzvah Yishuv HaAretz
Maharam Shik Yoreh Dead 225
Ohr Somayach, Letter for the book Shivat Zion, printed in Kol Yisrael, 5687
Rav Yitzhak Elchanan Spector, Letters, Shivat Zion
Chazon Ish, Letters 175
 See this article by Rav David Samson for elaboration on this topic.
 See this article by Rav Hershel Schacter for a halachic analysis of the sources regarding this mitzvah.