SSRS - Install Reporting Server (incl IIS) separate from SQL Server

We have to migrate our existing SSRS database from an old SQL server to our new SQL cluster. With this opportunity we would like to install de the reporting server on separate machine from the database. I have installed SQL Server Reporting Serv**ice** on a new server, but came to the conclustion that de tool uses the reporting server from the old database... Is it possible to have the reporting on a separate server including the web server?