Good for you for not going into denial and looking for advice. Many wouldn't.
This site may be useful especially if you share some of the stories on it with your son.
I would take it all very seriously but I wouldn't go piling in with a massive knee-jerk punishment.
You need to get him to understand the impact of his behaviour on the well-being of the other child and he won't listen if he's angry with you. I would be very, very hurt and disappointed about it so he feels bad about letting you and himself down.
I would also make sure I presented a very united front with the school so he knows any future episodes will be dealt with swiftly and effectively.
I would ask for a meeting with the school to discuss how to deal with it together and in the meantime I would start trying to work out why he is doing it.
Some children who bully are also being bullied themselves. Some have very low self esteem. Some are being pushed into it by other children who then stand back and watch knowing they won't get into trouble. Some are struggling to cope in other ways. Dig around a bit and see if anything like this is happening to your son. Do a lot of listening.
This must be a very hard time for you. I hope you find a way to deal with this and put it all behind you very soon.