Email during dns hosting change

Does anyone have any suggestions on what product and how to configure a mail server to simply redirect or relay mail to an exchange server on the internet? For example during an DNS hosting switch. We are moving offices and I want to setup a relay server in the old office with the old IP address to redirect mail to a server in a new office with new ip address. This way, before and after the hosting switch, mail will be directed to the new office and no down time.