。
Next year they will have been in America for ten years.
Literal
Next-year they [topic-は] America [in-に] 10-year being-[ことになります] (it-will-be-the-case-that).
~ことになる ('it will become the case that / it works out that') marks an objective fact or external decision about a future state. Here, paired with 10年いる ('to be [there] for 10 years'), it renders 'it will be 10 years that they've been there' — Japanese's way of expressing the cumulative-duration sense English uses the present perfect for.