I am just configuring a Linux Server Fedora 22 and have got sendmail to work: This was easy, just
sudo apt-get install sendmail (followed by)sudo sendmailconfig
then something like echo "My test email being sent from sendmail" | /usr/sbin/sendmail myemail@domain.com

I did a test email and this came back to my corporate email account, however I noticed that it went outside first (12+ hops) and then must have been sent back (another 12 hops) to my corporate exchange server.

The requirement of the Linux box is just to send emails internally when a process is complete (basically tracking activity). Thus the question is how and what do I configure to send the emails directly to our internal exchange server using sendmail

Typically we setup mail to "relay" to our MS Exchange server:

For Sendmail - To setup <myserver.mydomain> as relay:
a.) In /etc/mail uncomment the line below (remove "dnl" from start of line) in sendmail.mc and add myserver.mydomain so it reads:
define(`SMART_HOST', `myserver.mydomain')dnl
b.) After that run "make -C /etc/mail" This will add "DSmyserver.mydomain" to sendmail.cf.
Note: The sendmail.cf package must be installed for this work. The default sendmail package doesn't include the make ability.
c.) Run "service sendmail restart" after you've changed the above.

For the above to work your MS Admin must allow your host to relay as well.

Note that MS Exchange in the cloud (Office365) will show you multiple hops even if you are using an internal server for relay in a hybrid environment because it goes out to the cloud from your internal server.

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OK, Thanks
I thought it might be this file that needed adapting. I will give it a go!