Yes, you can do this.
- Copy all of the cloned VM's files from its directory, and place it on its destination datastore.
- In the VI client connected to the destination vCenter, go to the Inventory->Datastores view.
- Open the datastore browser for the datastore where you placed the VM's files.
- Find the .vmx file that you copied over and right-click it.
- Choose 'Register Virtual Machine', and follow whatever prompts ensue. (Depending on your version of vCenter, this may be 'Add to Inventory' or some other variant)
The VM registration process should finish with the cloned VM usable in the new vCenter!
Good luck!