I recently had to move some MS SQL databases from one cluster to another which contained some SQL reporting Services Databases. Having never done this before I decided to follow the Microsoft guideline:
1. Launch the “Reporting Services Configuration Manager”.
2. Login to the reports server for the database version.
3. Backup the encryption keys (enter any password).
4. Stop the Report Server Service.
5. Move the databases (both of them: ReportServer_name & ReportServer_nameTempDB) which ever way you feel comfortable doing - backup/restore, detach/attach.
6. Launch the “Reporting Services Configuration Manager” and login to the reports server again for the database version.
7. On the Database page, select “Change Database” and select “Choose and existing report server database” and enter the details of the new server.
8. Test the connection to make sure it’s successful and then select the corresponding database "ReportServer_name" from the drop-down and complete the steps.
9. On the Encryption Keys page, click “Restore” and add the file that was backed up earlier.
10. Restart the Report Server Service.
11. Check the URL's - http://server/Reports_Instance_Name/Pages/Folder.aspx