Amazon RDS now supports automating connectivity set up between an existing RDS or Aurora database and an EC2 compute instance

Starting today, you have the option to automatically set up connectivity between an existing Amazon Relational Database Services (Amazon RDS) or Amazon Aurora database and an Amazon Elastic Compute Cloud (Amazon EC2) compute instance. From the Amazon RDS console, you can choose an action to set up connection between your RDS or Aurora database and an EC2 instance. Amazon RDS automatically sets up your related network settings to enable a secure connection between the EC2 instance and the RDS database.

Source: AWS