You can set up an e-mail signature in Office365's OWA (also works with on-premise Exchange 2013 OWA) quite easily. While it's no problem to apply any kind of formatting to your signature, you'll find out that adding images is not as straight forward.

To set up an e-mail signature, follow the steps below.

For best results, use either Internet Explorer or Firefox. Google Chrome has some (minor) issues with OWA.

Log onto OWA. For Office365, this is https://outlook.office365.com/.

Click on the gear icon in the upper-right corner, and choose Options.

In the left tree, follow Mail > Layout > Email signature.

Edit your signature, or copy/paste it from another source (e.g. Word).
If you   ...