Here's a breakdown of the sentence:
* Je: I
* suis: am
* tombée: fallen (past participle of tomber, to fall)
* amoureuse: in love (feminine form)
* de: of
* toi: you
Important: The verb "tomber" (to fall) is used with the preposition "de" when expressing falling in love.
You can also use the more formal "je suis tombée amoureuse de vous" if you are speaking to someone you are addressing formally.