We have a web app that allows users to log in with their on premises active directory into our app.
We want our users to be automatically logged into office 365 when they access our app.
I have looked at Azure active directory and my current understanding is that if active directory is linked to azure with Azure active directory connect we will be able to use Azure single sign on to auth users and they will automatically be signed into office 365 and any other connected apps.
Is this correct? or is this not the correct method of setting up SSO for office 365?
Yes, you can create a Single Sign-On between the on-premise directory and Azure Active Directory. You can use identity federation (your on-premise directory does the authentication) or synchronization (AAD does it from the information you synched)
An example: http://azure.microsoft.com/blog/2012/08/06/implementing-single-sign-on-with-windows-azure-active-directory/