We have left out Rambam's statement, "one who accepts them is called a Ger Toshav (Hebrew term translated as Gentile Resident of the Holy Land)," and all the laws of the Ger Toshav, because they do not apply when the observance of the 50-year cycle of Jubilee in the Land of Israel is suspended, as Rambam writes in Laws of the Worship of Stars (and Idols) 10:6. If a Gentile declares his acceptance of the Noahide Commandments before three observant Jewish men, it does not change anything in regard to his obligation to observe the Noahide Code, or his merit to be called one of the Pious of the Nations (Hassidei Umot Ha'Olom, in Hebrew). This formal declaration of acceptance only permits the Jews to allow this Gentile to live as a resident in the Land of Israel in accordance with Torah Law. See Likkutei Sihot, vol. 26, p. 134 (and Tzafnat Pane'ah on Hilhot Issurei Bi'ah ch. 14), which explains that this is the opinion of Rambam. This appears to also be the opinion of Rashba in Torat Habayit, quoted in Beit Yosef Yoreh De'ah ch. 124: "And we do not require him to accept them in front of a Jewish Court of three..."
It seems clear from Kesef Mishneh on Hilhot Avodat Kohavim ch. 10, that Rambam rules that nowadays, if a Gentile wants to act as a Ger Toshav by keeping the Noahide Code, Jews should not prevent him from living in Israel.
This does not seem to be the opinion of Ramban and Ritva in Tractate Makot 9, who say that a Gentile is not "fulfilling a commandment" unless he accepts them before a Jewish Court of three, and then is he called a Ger Toshav. (They may mean that this applies when all the Jews are gathered to Israel and the Jubilee cycle is in effect, for then Gentiles will need to make this declaration to be granted residence in Israel; nowadays, however, it may not make any difference in their obligation to observe these commandments.)
The question on their opinion arises because it is unclear whether they hold like Rambam that the literal Ger Toshav status does not apply in our days, and therefore we come to the conclusion that this declaration makes no practical difference, or if they hold like Ra'avad (Laws of Forbidden Sexual Relations, ch. 14) that there is a concept, and the granting, of a Ger Toshav status even in our times. If Ramban and Ritva hold like Ra'avad, it would be obvious that their opinion is that this is the only true way to fully accept the Noahide Commandments, and they would then say that this also applies nowadays (the Divine Code by Rabbi Moshe Weiner, Ask Noah International, 2011, p 64-65).