Is the storage (SAN) vendor managing the remote data center by any chance?
NetApp or EMC for example?
They might have a migration process.
What virtualization software does the data center use? Hyper-V also? If it is the same, that would facilitate matters to some extent.
How much downtime can you accept (if the databases had to be dismounted and then mounted in the new location)?
If the amount of data is significant (hundreds of GBs, or even TBs) copying the data over the Internet may be slow.
What kind of Internet access do you have? And link to the remote data center?
How close is the remote data center?
Is Active Directory remaining on-premises?
In theory, you could dismount the databases and the Exchange VM and then mount them / reattach databases in the remote data center but...
- How will Exchange talk to Active Directory?
- You'll need to adjust DNS
There's more questions there than answers but maybe if you describe the environment a bit more someone would be in a better position to make recommendations.
The smoothest transition would be a hybrid environment where you could move mailboxes gradually and then remove the on-premises Exchange hardware once finished.
This type of migration seems less typical than Exchange migrations to O365, Intermedia, AppRiver, SherWeb, etc..
Have you considered something like that?