Forging a signature is definitely something warranting a consequence.
If it is possible, try to see if he is having difficulties with the school work of if he simply does not feel motivated to do it. That would make a difference.
If he had never lied before and had in the past done well in school, it may be helpful to inquire as to the most current behavior and motivation behind it.
Punishment does not allow for one to correct ones behavior. I rather prefer calling it a consequence where the person has a chance to prove oneself and be acknowledge and or praised for it. If he has any special privileges, those may be used as consequences (taking those away until the behavior improves) Of course, always let him know how to earn the privileges and have a reasonable time frame that would be a motivator for him. Always follow up with your consequences and rewards in a consistent way.
You are right he should have come to you earlier but that can be blamed on his youth.
Try to see if there is a guidance counselor at school that can assist him. Apology to teachers may be appropriate as well. School usually provider a counselor so it may be a good idea to connect with the one at the school. If that is not an option, your insurance may give you a referral to someone that can work with him (if he is willing to do go to counseling) The school counselor should be able to address the issues as well as the guidance counselor (unless the school uses the same person for both titles)
Just encouraging him and pointing out that this is something that happens to others, having him focus on the things that he has control over (such as making up work, talking to teachers and working on his honesty) Let him know that you are there for him and that you understand that young people make mistakes in their life-that's how they learn and that you would back him up and support him as long as he puts forth an effort.
It is best that he focuses on the positive and things that are within his control. He could ask teachers and the school counselor for some tips on how other students in his shoes had been able to move forward. Teachers usually understand when someone had been ill and adjust their work accordingly.