1. Follow KB 842425 to move RS DB to a new instance.
2. Ensure that you have a login for the TFS Reports account, in case your RS databases are now going to hosted on a different SQL instance. The login for the RS database should have RSExecRole in Report Server databases (which it should retain when you restore the RS databases.)
3. Create new data connections for TfsReportsDS & TfsOlapReportsDS if required. (Refer to here http://social.msdn.microsoft.com/Forums/en-US/tfsreporting/thread/fc53be12-2ebd-41c8-a66a-ccd4437033fd)
4. Run TfsAdminUtil ConfigureConnections command to update setting /ReportsUri and /ReportServerUri. Consider http://support.microsoft.com/kb/959126 while doing it.
5. Run the TFSWSSConfig.exe on the SharePoint instance to update the reports redirector.
6. On the AT, edit the MSIProperty.ini file & change the RS machine name for the VSTF_RS_SERVER property. You just need to give new machine\server name for RS & do not give the instance name. Optionally update the VSTF_RS_REPORTS_URI, & VSTF_RS_REPORTSERVER_URI properties.