A simple backup and restore of the ReportServer database would do it, ensure you follow this guide https://docs.microsoft.com/en-us/sql/reporting-services/install-windows/migrate-a-reporting-services-installation-native-mode or this guide https://docs.microsoft.com/en-us/sql/reporting-services/install-windows/migrate-a-reporting-services-installation-sharepoint-mode depending if your in native or sharepoint mode.

The better option would be to upgrade the solutions used originally to deploy the reports to the latest SSDT / Visual Studio code base and re-deploy, if you don't have the solutions, I would advise you download all the reports, create a solution and put it in source control somewhere for additional security.