1. Stop ArcGIS Server on the new Machine (say this is MachineName2)
2. Copy the server object configuration files from the old machine at <Machine1 ArcGIS Install location>\Server\user\cfg and paste them in the new machine at <Machine2 ArcGIS Install location>\Server\user\cfg.
3. Edit the configuration files to replace <MachineName1> with <MachineName2>
4. Start the ArcGIS Server Machine2.