Best way for UI program to check for internal event

Best way for UI program to check for internal event

I have a WinForms application that is the UI layer running over the logic
layers.
My application is a client-server IM program. When the internal program
accepts an incoming connection request I'd like the UI to be updated by a
simple button text change.
One way to do this would be to expose an internal boolean that is changed
by the logic layer when it has processed a request and is constantly
checked by the UI on its own thread.
This doesn't seem like the best way to me, I assume there are much better
built in ways for doing this?