Star with going to www.office.com to reach the Office 365 homepage. From the office 365 homepage click on the outlook application to access Outlook's settings.
From the office inbox menu, click on the gear symbol on the right-hand side of the page, for outlook settings.
Once in outlook settings, click on the link "View all Outlook Settings"
to get to the signature option from main outlook settings go to:
B. Compose and reply
Afterwards save changes and you are set too have your own personal signature from the Outlook web application.