Use the below listed guide to change the outgoing mail IP address for the entire server:
Log into WHM and go to the 'Exim Configuration Manager'

Select the 'Domains and IPs' section, and make sure the options match the ones shown in the screenshot below.

SSH to the server and edit the /etc/mailips file in your favourite command line text editor. If you're unsure of which text editor to use, 'nano' is the easiest for beginners.
root@server ~]# nano /etc/mailips
Edit the file to make sure it looks like this:
*: 123.123.123.123(Make sure you replace 123.123.123.123 with the actual IP address you wish to send email from).
Save the file.
That's it! Your Exim mail server will now send email from the IP address you've specified in the /etc/mailips file.
Please Note!
You will need to make sure your domain's SPF record specifies the new IP address or your email may not be accepted by the receiving host. i.e. "v=spf1 a mx ip4:123.123.123.123 ~all"