I'd recommend looking into our EC2 Image Builder. You can take an existing golden EC2 image and create an image pipeline for Docker, including an output to our Elastic Container Registry. ECR not only does security and vulnerability checks on your images, but also integrates nicely with Amazon ECS. Once the Docker image has been created from EC2 Image Builder and is stored in ECR, you'd create an ECS cluster (either using EC2 or Fargate), configure your tasks and scaling policies, as well as a load balancer, target group, etc. in front of ECS, and that's the vast majority of the work. We have some good tutorials for common tasks with ECS you can reference.
If you want a detailed walk through of moving an EC2 application over to ECS, we also have an Introduction to ECS Workshop. This workshop includes a section dedicated to migrating an application from EC2 over to ECS. I personally would start with the EC2 Image Builder approach as the Workshop uses a lot of third-party CLI tools which can be difficult to follow, whereas the documentation for EC2 Image Builder seems much more straightforward.
There are numerous resources available, i.e. AWS modern-app portal with multiple use-cases and guides, this white paper which leans toward EKS/k8s, etc. Overall it is a very broad question, options would depend on the current platform (windows/linux), framework/language used (i.e. we have app2container migration tool for .Net and Java apps), application architecture (monolith or not, stateful or stateless, horisontally scalable or not, etc).
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