migrating emails

I wonder if the title makes justice to my question.

If a company has its emails set up with Microsoft Exchange server with email ids ending as: user1@company.com

Now if, for some reasons, they decide to shift onto a new domain (also say a newcompany name), i want to receive all the mails at the the address user1@newCompany.com

I also want my old mails from the user1@company.com email address. What is the best way to migrate without any glitches?