AWS RDS databases & SSIS
You can use several ETL tools for this, it could be on premies, or cloud based, final decision always depends from cost, corporate standards and many other moments

good starting point as most close to Your request:


Informatica Cloud -
https://marketplace.informatica.com/mpresources/docs/Implementing_DWH_on_AWS_in_Hybrid_Env.pdf
Talend Cloud - https://www.talend.com/products/integration-cloud 
Community version of Talend as well could be installed on any VPS and
connect to cloud databases


Any tools and recommendations always depends from personal experience and of course on the market You can find more commercial and open source tools