The same thing that routes email in a Unix environment (or should be, anyway) -- the MX record in your DNS system (or your ISPs DNS system, if they are hosting DNS for you).
But if it's your only mail server, it's not really routing email internally. You'll just configure your mail client to connect to the Exchange box with the desired protocol (POP3, IMAP, MAPI for Outlook).
Most likely you have your firewall configured to forward SMTP traffic (25) to a specific IP address, so you'll either need to make the Exchange box have the same IP as the retired Unix box, or (better) change the firewalll NAT rule to point to the new IP address of the Exchange server. (And if you're not running the Exchange box behind a firewall, you need to stop doing that now.)
Likely your external DNS A and MX records are already pointing to the public IP referenced in the firewall NAT rule. There should be an A record (eg mail.mydomain.com) and an MX record that points to the name specified in the A record.
If you do have multiple internal mail servers and want to relay email between them, you'll have to add their IP addresses to the SMTP connector in Exchange. By default, Exchange 2000 is not an open relay.
If you have lots of users or lots of email, you may want to seriously consider upgrading to Server2k3/Exchange2k3. Exchange 2000 Standard still has a 16GB limit on total email. 2003 ups that to 75GB.