I've been living with my boyfriend for the past 8 months and we have two cats, I've found a place to live that has pets, but he won't let me stay until I get in my new place

He will have to evict you on a formal basis he can't just kick you out. Local law will dictate what steps need to be taken to evict you.

If he refuses to allow you in the home, you call the police and prove you were living there.