He is black by tradition and history. Actually, there are very few 100% black in US and I don't know what that means any way. In the old South, by (a now infamous) law, one was considered black if one had 1/8 black blood. They had to have this law so they could legally decide whether they could enslave someone--You could only enslave a person with more than 1/8 black blood (actually I am not sure if it is "greater than" or "greater or equal to" 1/8, as one can see this subtlety makes a huge difference to one's life back in the old South)
Nowadays, the only way you can tell whether someone is black is by the way he or she looks and Obama looks black.