How to connect with host PostgreSQL from vagrant virtualbox machine
You can reach your host from your guest by using the default gateway on your VM.
See this answer for an explanation.
By running netstat -rn you can get the default gateway and then use that ip address in your config file of your application.
Running netstat -rn | grep "^0.0.0.0 " | cut -d " " -f10 should give you the correct ip address. (only tested this on my machine)
Easy way - simply use this "magic" IP from inside of vagrant without any additional configurations:
10.0.2.2
Don't know if it's always static, though for me works and it's very convenient - I can use laptop at home, from office - having assigned different IPs to me by routers, but my VMs know the "trusty name" of their master 🐶