AWS Database Migration Service (DMS) offers free use for 6 months per instance if you're migrating to Amazon Aurora, Amazon Redshift or Amazon DynamoDB.

Amazon Aurora is a fully managed, MySQL and PostgreSQL compatible relational database built for the cloud, that combines the performance and availability of high-end commercial databases with the simplicity and cost-effectiveness of open source databases. Aurora is up to five times faster than standard MySQL databases and three times faster than standard PostgreSQL databases. It provides the security, availability, and reliability of commercial-grade databases at 1/10th the cost.

Amazon DynamoDB is a fully managed, multi-region, multi-master database that provides consistent single-digit millisecond latency, and offers built-in security, backup and restore, and in-memory caching. DynamoDB automatically scales throughput up or down, and continuously backs up your data for protection. DynamoDB gives your globally distributed applications fast access to local data by replicating tables across multiple AWS Regions

Amazon Redshift is a fast, scalable data warehouse that makes it simple and cost-effective to analyze all your data across your data warehouse and data lake. Redshift delivers ten times faster performance than other data warehouses. You can setup and deploy a new data warehouse in minutes, and run queries across petabytes of data in your Redshift data warehouse, and exabytes of data in your data lake built on Amazon S3.

Free use of DMS and AWS Schema Conversion Tool (SCT) is available for 6 months (183 days) from the time you start a DMS instance. Supported Instance Types are t2.micro, t2.small, t2.medium, t2.large and c4.large.