Microsoft Azure SQL is the one of several cloud platforms on the market. It has a strong Hybrid Cloud capability that allow your on-premises applications to use cloud services, such as the cloud database and storage service.
MS Azure stores data in the same manner as SQL Server (tables, indexes, views) and thus will be familiar to Windows DBAs, but your SQL Azure Server is spread across multiple physical computers for more flexibility. Azure SQL operates in many regions across the world and can be scaled easily from 10 to 10 million users without any additional coding.
DBConvert and DBSync applications simplify the exchange of data between Microsoft SQL Azure and other Cloud databases or on-premises databases. It allows two-way data transfer in almost any format, including MySQL, Oracle, PostgreSQL, DB2, Amazon RDS, Maria DB, JSON and others.
To narrow your search have a look at products listed above. In addition to On-premise database migration you can easily move and replicate data between Microsoft Azure instance and many other directions.