In the large companies this is not an uncommon for employees to want to transfer. Sometimes it is to switch job titles, sometimes to switch projects, and sometimes to switch work locations. In many cases this process is started without the current management knowing.
First of all make sure you are allowed to switch. Some companies restrict movement for 6 months or a year if you just moved or were given a promotion.
If your annual review is coming up discuss it then. Don't say you want to switch parts of the company, but talk about options within his department, or within his bosses department. Talk about things that can happen in the next year or two.
Investigate how the company hires from within. Many companies have a career development site on their intranet. Most hiring mangers will not alert your current boss in the first few stages of the process.
Sometimes you can be matrixed to another part of the company for a project. Your current boss is still your boss, but for the duration of the project you support the new project. That can be viewed by the other organization as an audition. Eventually if they see your potential they will ask for you to make the switch. You can tell your current boss that helping the new project will help the company, increase profits, and impress the customer. To find these possibilities use your network of friends within the company to look for positions that may only exist for 6 months or so.
You don't have to tell your current boss that you applied. If the system is setup to allow bosses to fire employees that applied for internal positions the odds are that the organization will always have a lot of turnover, and not for the right reasons.