If there is a way it's probably painful, involves third party software and may not work even then.. or at least that was my experience last time I tried it, which was admittedly, some time ago..
Easiest, if you can, is to set up a new (temporary) IMAP mail account in Outlook Express and move/copy your mail to that account - this then stores all the emails on the host server in a standard format that just about any mail app can access. Depending on how much mail you have and the network speed available, it may take a while for all of it to upload.
Set up Mail / Outlook on the Mac to use the same IMAP account and all of your mail will download to the new machine.
Set up your original mail account on the new machine too, and drag the folders across into it.
(Personally I'd recommend you set that up as an IMAP account too, if your host allows it - that way their mail server acts as your backup, and it also means you can set up and access synchronised mail on multiple machines/devices)
Delete the second (temporary) IMAP account.