Migration of VMs from vCenter 5.1 to vCenter 6.0

My recommendation is just move the vSphere ESXi that are managed by the vCenter 5.1 to the vCenter 6.0. Once with the old hosts on the new vCenter, you can migrate the virtual machines from the old 5.1 hosts to the new 6.0 hosts.

For specific details on how to move an ESXi host from one vCenter to another, take a look at the following VMware KB article: https://kb.vmware.com/selfservice/microsites/search.do?language=en_US&cmd=displayKC&externalId=1004775

The link is simply asking to remove the Hosts and add them to the new vCenter. Here, in my scenario can I add existing 5.1 ESXi hosts to vCenter 6.0?

Yes, you can. vCenter Server 6.0 can manage hosts from version 5.x to 6.0.

Okay. Will all VMs be automatically moved to the vCenter 6.0 console after moving ESXi hosts to 6.0?

We have another plan-
Instead of moving 5.1 ESXi hosts if we build new 6.0 ESXi hosts, can I then move 5.1 VMs in 6.0? We have approx 1200 VMs running in 5.1.

Sorry, maybe I misunderstood your question. You just want upgrade your vCenter Server from version 5.1 to 6.0? If yes, it is very simple and you should not worry about the virtual machines.

About the upgrade to vCenter Server 6, it will be transparent to your virtual machines, but you need to make sure you follow the best practices on how to upgrade the vCenter Server to version 6.0, that will include compatibility with the OS and DB where the vCenter Server 5.1 is running.

The following KB article shows the best practices of upgrading to vCenter Server 6.0: https://kb.vmware.com/selfservice/microsites/search.do?language=en_US&cmd=displayKC&externalId=2109772

No, I am not talking about upgrading 5.1 to 6.0. I want a new vCenter server on a separate hardware.

Quite simply, Disassociate your Current hosts from vCenter Server, by selecting remove host when connected to vCenter Server.

This does not affect running VMs or Hosts.

Then install vCenter Server, and Add Hosts.

see my EE Articles

HOW TO: Deploy and Install the VMWARE vCenter Server Appliance 6.0 (VCSA 6.0)

HOW TO: Add VMware vSphere Hypervisor ESXi Hosts to VMware vSphere vCenter Server 6.0

HOW TO: Install and Configure VMware vSphere vCenter Server 6.0 for Windows

Thank you so much for all your clarifications. I have another few question for which I want your expert comments-

1. For vCenter 6.0 do I have to point to the same storage which is using by vCenter 5.1 ESXi hosts so that VMs can be shown in vCenter 6.0 console?

2. If we allocate new SAN storage for 6.0 ESXi hosts, will adding of existing 5.1 hosts to 6.0 vCenter automatically move existing VMs in 6.0 vCenter?

3. If I freshly install ESXi 6.0 on new upgraded hardware in vCenter 6.0, what is the best way to move VMs residing in ESXi 5.1? We have approx 1200 VMs running in 5.1.