Here's a feature on Azure Portal that allows easy porting of existing databases from On-Premise to Azure SQL Database Managed Instance .
Here's a demo on the tasks required to port an On-Premise database to Azure SQL Database Managed Instance:
It's a great offering for organizations to "lift and shift" existing databases to Azure with minimal impact, yet provide many of the great features from Azure. Using VNET your data is security in transit. Active Directory integration and private IP address' included as well. There's also a Data Migration utility within Azure to port your data seamlessly.
To summarize, Azure SQL Database Managed Instance is the closest thing to Enterprise SQL Server On-Premise available today.