Basically, this is possible. If your particular webapp is capable of handling this depends on your environment and if this webapp is prepared for this.
Some questions: Do you use Active Directory for authentication? What is your webserver? IIS on Windows, Apache on Linux? Something else? What are the apps? What auth methods do they offer?
The most important thing you should research in this regard is Kerberos, which is used by Active Directory (and many other things) for exactly this purpose: Single sign on.
Regardless of the technology, prepare for a challenging experience, as doing this right is quite difficult.