Use the Repoting services configuration manager on the system you want to move.

Backup the RS encryption cert . Backup the RS and RSTEMPdb with copy.

Install SSRS on new machice. Restore original db from server RS and RStemp. Use SSRS config manager to restore the cert.

Make sure dbs referenced in the data soiurces are present on the server.

Restart SSRS services.

Lots of information on the net for this process.