To install Email Signature in Outlook on your Web App, please follow these steps:
Make sure to use Chrome Browser (Safari or Firefox will mess up the formatting).
Click on the 'Copy Signature' button to copy your signature to the clipboard.
In Outlook Web, click on the 'Cog' (Settings) icon and go to the 'View All Outlook Settings' option.
In the 'Mail' menu, go to the 'Compose and reply' tab to find the 'Email Signature' option.
Click inside the text box, and Paste your Email Signature (ctrl+v for Windows or cmd+v for Mac).
Tick the two options below the text box & click on the 'Save' button to save the changes.
And that's it. Compose an email & your Email Signature will be right in place.
Good work there, you!