Forgot to get other parties insurance information

Got into an accident on my way to work last night. I was super flustered, it was my first accident ever & i was at fault so I just gave him my insurance info. It was minor damages/ a fender bender but I realized after i was at work & calmed down that I never got his name or insurance info. How can I proceed? Tell my insurance? Wait for his insurance to contact mine?

Thanks so much in advance.