I agree with GG. Moved (in) next door to me.
I dont' agree that settle is an appropriate word here. We don't use settle to refer directly to moving house - it is more to do with moving area. If you moved from Number 2 to Number 4 Lilac Road, you wouldn't talk about having settled next door. You moved there.
settle (LIVE) Show phonetics
verb
1 [I usually + adverb or preposition] to go and live somewhere, especially permanently:
After they got married, they settled in Brighton.
Are you getting this confused with the phrasal verb 'settled in'
settle in phrasal verb
to become familiar with new surroundings, such as a new house, job or school, and to feel comfortable and happy there:
Once we've settled in, you must come round for dinner.