There's a number of schools offering training in Medical Informatics (MI) across the U.S. These include Stanford, OHSU, Pittsburg, Columbia, UAB, etc.
Different schools have different requirements. Some will take bachelor's degrees, others require professional degrees like M.D., D.D.S., registered nurse, etc.
Different schools offer different training courses. Some have Ph.D. programs, masters, certification, etc.
But wait, there's more.
Different schools have different opinions on what constitutes Medical Informatics. Therefore each program will emphasize different areas of the larger MI field. Example, last I checked, UAB's program focused on turning out Chief Information Officers (CIOs). This could have changed since the technology economy downturn or I could have just misinterpreted their mission. You'll see a wide diversity of program emphasis.
On a personal note, some aspects I've seen covered in the MI field are:
Computer programming: Mostly because the medical field has become dependent on technology. Very helpful to understand the CS part of it. Nice that you have a CS background.
Organizational behavior: Key part. Doctors are people. Patients are people. All healthcare professionals are people. Lump them into a group and you start seeing behavior patterns like any other business. Helps in understanding why certain phenomena occur. Ex: why we don't have a robust computerized patient record and still resort to paper. Why Physician Order Entry (POE) is still hard to implement.
Bioinformatics: Most people seem to already know about this area. It sometimes falls under the Medical Informatics umbrella.
Information Science: Medicine is information intensive so it helps to understand what constitutes information so that you can manipulate it. Something interesting I learned in regards to medical literature publishing is that there's a pattern of publishing only the positive results (people like to see articles on Drug X curing Disease Y, not Drug A failing to cure Disease B). This leads to a bias in the information that's covered by medical literature. Since most articles cite previous published work, you can see there's ramifications for future research.
Sorry for the long blah blah. Hope it helps or is somewhat interesting.