Virtualization comes so handy and I believe is the best start. It is a process that can happen on a very controllable pace.
The initial target would be virtualizing every system residing on a physical server. While doing so, you can take advantage of the ability to create as many virtual machines as you need and this number can be much bigger than what you currently have as physical machines.
This would allow you to achieve better governance by designating a virtual box for every server role within the organization where this was too costly when living in the physical world.
The next step would be signing up with a cloud provider, then bridging your internal network with the cloud.
Finally you can start moving ‘migrating’ machines to the cloud.
Cloud offers virtual machines as one of the many other services. So, later on you would consider eliminating certain virtual machines and utilize specific optimized cloud services such as web servers or cloud database engines, eliminating the use of virtual machines to run those roles as cloud services are already always optimized, patched, load balanced, etc.