When you are using Virtual Private Networks (VPNs) to connect to cloud solutions via the internet, you connect your cloud services to your network like additional VPN sites. For most IaaS scenarios, that is totally fine, but when you are using PaaS or SaaS solutions, they often have no VPN endpoints, and the security comes from encryption and identity and access management. 

Cloud services are built on zero trust networks, which means that the security does not come from an IP or network security; it comes from protocols and identity. To learn more about zero trust architectures, I highly recommend the article at https://www.paloaltonetworks.com/cyberpedia/what-is-a-zero-trust-architecture.

Nevertheless, you are able to connect cloud providers with each other via VPNs. For most cloud providers, you would use standard VPN protocols, like IPSec. 

The following article shows the setup for connecting AWS to Azure: https://blogs.technet.microsoft.com/canitpro/2016/01/11/step-by-step-connect-your-aws-and-azure-environments-with-a-vpn-tunnel/.