I worked for an eye doctor, and we were prescribing contacts all the time to people who needed bifocals. They have bifocal contact lenses, and they have progressive contact lenses. The bifocals of course have just your distance and your reading rx. The progressive lenses will include your computer rx as well. (You generally read closer up than the computer screen is) It will all depend on what your prescription is, and what you need. They also as some others mentioned, have monovision. This is where the doctor prescribes one contact for one eye to have a reading rx, and the other for your distance. This works pretty well too.
You will want to get an appointment with your doctor so he can fit your for contacts. You'll want to keep in mind that it may take a little bit to get used to the contacts, not just because you will be accommodating for your reading and distance, but also because they are contacts. Some brands feel better on some people than others, and if you don't like the first ones, go back for a follow-up and let your dr know.