Answer: I am good.
Explanation: I am well can be used sometimes but I am good is the proper way. I am DOING well is better for I am well. Also, I am good is used more often.
"I'm well" is also allowed but not for the reasons many think. That response only works if "well" takes on its adjectival form, meaning "in good health" or "good or satisfactory." Now, if someone asks "How are you doing?" "I'm doing well" is the correct response.
Hope I helped!