Impact on SSRS of migration of SQL Server from 2008 to 2012
Your SSRS deployment just needs access to two databases ReportServer and ReportServerTempDB. It doesn't matter where they are hosted as long as they are accessible.

When you move these databases to the new server you will need to open Reporting Services Configuration Manager and redirect SSRS to the new SQL 2012 server. You can change the connection on the database tab.

If the connection test goes through OK then you should be ready to go.

One thing to make sure of is that all the logins from the old server are present on the new server before transferring the databases. If they are not the permissions for any missing users will be dropped.