Amazon ElastiCache now supports online data migration from Redis on Amazon EC2
You can now use ElastiCache data migration feature to migrate your data from self-hosted Redis on Amazon EC2 to fully-managed ElastiCache cluster-mode disabled configuration. With this feature, once you provide ElastiCache-accessible endpoint and port of your Redis cluster, ElastiCache will replicate the data from your cluster in real-time to your ElastiCache cluster. Once the data sync is complete, you can update your client applications to start using the newly-populated ElastiCache cluster.
Source:: Amazon AWS