As of tomorrow it will have rained for a week straight.

Literal

Tomorrow [with-で] 1-week rain [subject-が] continue [nominalizer-事] [dative-に] become.

The same ~ことになる pattern, with 雨 ('rain') as the subject and the simple verb 続く ('continue') instead of the compound 降り続く. The literal is 'rain continues' rather than 'continue raining' — slightly looser, more conversational phrasing.