1. Create a new email message by clicking New E-mail under Home tab.
2. Compose your email. (Note: make sure that there are hyperlinks existing in your email body) See screenshot:
3. Click Format Text tab, and then go to Style group, and click 
button under Change Styles. See screenshot:
4. Then a Styles dialog pops up. In this dialog, please put your cursor on the Hyperlink field to show the drop down button.
5. Then click the drop down button 
, and select Modify from the drop down menu.
6. In the Modify Style dialog, you can do as follows:
A: If you don’t want to show an underline below the text, please click 
button.
B: Choose your desired color in this color field 
.
C: If you just want to change the hyperlink color in the current document, please keep the Only in this document box checked; And if you want to apply this changes to the new emails you will compose next time, please check the New document based on this template box. See screenshot:
Note: The above operation can be used in Outlook 2007, 2010 and 2013, 2016 and 2019.
7. After configuring all the settings, please click OK to close the dialog. And the color of the hyperlink texts have been changed as your wanted color. See screenshot:
