The straight translation from "Tuu mun vaimoksein" would be "become my wife", but there's a good reason why I decided to do it like this. In Finnish it's more typical to ask "Will you become my wife?" instead of "Will you marry me?" (naturally it doesn't work if the person you're asking this is a man). In English it sounds much smoother and just generally better to ask someone to marry you instead asking them to directly become your wife or husband.
Olavi Uusivirta Tuu mun vaimoksein English translation