I cut off my ex and now he's mad

So for a bit of background my ex cheated on me with my best friend and they are currently dating, he was super toxic during our relationship and I didn't find out about the cheating until after he broke up with me. Today I finally cut him off letting him know that if he tries to contact me further I will file for harassment which is not something I wanna do but he hasn't been leaving me alone so I felt as if I had no other choice. Welllll apparently that didn't sit well with him and I found out he went on a rant about me claiming he was gonna drag me to court and all this other nonsense. I don't know whether to laugh or take it seriously. My fear is he will try and to keep harassing me, he knows where I work and where I'm staying currently. Should I just wait for something to happen??? Like I can't just call the cops on him for being mad.