Next March, I'll have lived in Kyoto for eight years.

Literal

Next-year [possessive-の] March [at-で] Kyoto [in-に] 8-year lived-[ことになる] (it-will-be-the-case).

~ことになる ('it will turn out / it will be the case that') is Japanese's standard frame for cumulative duration anchored to a future point — 'as of next March, the case will be that I lived 8 years.' 住む takes に for the place of residence. 住んだ in past plain form, not the stative 住んでいる, because the duration is what's being totaled, not the current ongoing state.