Technically, speaking, yes they do. However, do they for the layperson? The answer is a very strong, "probably not." If you want them to fit then be ready to do some work because they can be modified to fit the C6. However, you cannot get a full seat for the C6 because the seats are intended for the C7. Yet, there have been multitudes who have added the C7 seats to their C6 with great success. But you need some elbow grease and some know how to enable you to do this task. If you are a beginner and do not know anything about this kind of work then you might want to learn a little bit and come back. Your Corvette is a large investment in your fun, after all. It would be terrible to damage it on accident, especially if you do not have the knowledge necessary to make the changes you want to be done.
You might have to change the track and the electric set-up. The shape is the same, which is great news for you, however, getting things to work right might be the problem. For example, if you want the seat to warm then you are going to have to figure out how to hook it up to the existing wiring. The honest truth about that is that you are going to have to rewire everything to get the right effect. Unfortunately, the C6 and C7 have different wiring schemes and understanding them and hooking up with them properly is essential to getting the job done right.
Click here to see the C7 seat kit.