There are several ways depending on how certain you are that you will be there, but I am pretty certain that "sunde iru" will work for the future (will be living in) as well.
Elizabeth is correct. It is perfectly acceptable to say:
来年、日本に住んでいます。
予定
Also, could i get some furigana/meaning for these kanji?
予定 よてい yotei: plan(s), as in something you are planning to do
Did you want to use 「てもらいます」expression?
Then it is, 「住まわせてもらいます」.
Rather than 住まわせてもらいます, it is more acceptable in modern Japanese to use 住ませてもらいます. For type 1 verbs, you use the 未然形, mizenkei, form of the verb and add せてもらいます. Mizenkei is the plain, negative form with the ない at the end dropped off.
Examples:
住むーー） 住まないーー） 住ませてもらいます
行くーー） 行かないーー） 行かせてもらいます
For type 2 verbs, you use the 未然形 as well, but add させてもらいます。
Examples:
食べるーー） 食べないーー） 食べさせてもらいます
浴びるーー） 浴びないーー） 浴びさせてもらいます
Irregular verbs have their own rules.
Examples:
するーー） させてもらいます
来るーー） 来させてもらいます (こさせてもらいます）
Also, you can replace もらいます with いただきます to be even more humble if the situation demands it.
It means that someone is going to let you stay.
It should also be pointed out that the above form isn't only used in the situation where someone is directly giving you permission. It's also used to be more humble about your own actions.