Found the solution myself. Apparently in Azure VM's any time you change dns settings, the host needs to be rebooted. I'm just so used to physical host not needing reboot.
Using on prem DNS Server
I setup Site-To-Site VPN from my on prem network to Azure. Right now I only have singe VM running in Azure that I'm using for testing. I'm able to ping and RDP from Azure VM to hosts on prem without any issues using private IP addresses. I can also RDP and ping my VM in Azure from on prem host without any problems. From my Azure VM I successfully ran nslookup command against my on prem DNS servers and received response for my internal hosts as well as www sites. Here is my problem. As soon as I change dns address on the Azure VM host to point to my DNS servers on prem, all of my connections to the Azure VM, RDP, SSH, Bastion go down and there is no way to connect to the host again. This is a test server so I tried to disable firewall on the host and configured nsg to allow all traffic. I appreciate any help I can get.