j2ee application needs to migrate to a cluster

I've got a j2ee application that currently runs on a tomcat on a single server. This is going to change and the j2ee app will move to a cluster environment. This clustering environment will support failover mechanism so that always a node can host the application.

There is also a hardware load balancer to offer additional stability.

My question is, since my application is stateful(there are sessions and cookies for each user, page etc.) how will the load balancing can be achieved? For example what will happen when the server that hosts the application will fail and there are some open sessions. The application will start on another node but the sessions will have been lost.

Is this something that relies on the specific application server(JBoss, Tomcat etc.)? Do I need to implement a software solution in the application level that can support load balancing(i.e. handles open sessions, cookies etc)?