Preface: I have been in the field for 11+ years, and have been leading front end dev teams for 3+ years a large companies such as Nike.
I disagree with the previous answers on a few of their points. (This is assuming based on the fact that you said you're mentoring him that you're also his lead, if not and by boss you mean the lead developer than listen to the previous answers and go talk to them, if by boss you mean a owner, department head or some other non developer then continue reading)
Firstly: I would NOT go to your boss. You should view going to your boss as a nuclear option to be reserved as an absolute last resort. You boss had confidence in your ability to mentor this dev and handle things like this. Every time you come to your boss to have him handle something like this it is going to erode a little bit of the confidence away. I assure you your boss has much better things to do than dictate code standards. Only involve your boss if you need clarification on something or things need to be escalated to the point of a formal reprimand or dismissal.
Secondly: this isn't a company policy decision. Code formatting and code standards are entirely at the discretion of the lead developer. You boss does not care or need to care about nuances like formatting and comments.
Thirdly: This is not common, In 11 + years I have only ever ran into one company that would allow leaving comments in code for history. The only places I would expect to see this type of coding is a outdated shop that ignore best practices and has no source control, PRs or GIT repos, and if that's the case, RUN run far far away and don't ever look back.
If I were you I'd first give him a tour of GIT and show him how it works since he clearly doesn't understand commit history. Hopefully that helps ease his concerns and makes him understand where you're coming from when you say not to do it and that will be the end of it.
Second I would refuse to approve any of his PRs until he follows your suggestions, you're the lead, so lead. If the code doesn't meet your standards then it shouldn't be merged, it's that simple.
If he still refuses to change it and lets his PRs sit out forever with you blocking it then it's time to talk with your boss about the dev. Maybe have the boss tell him to listen to you, or write him up or possibly even dismissal depending on how he reacts and his overall performance.
You're his mentor and if he's refusing to listen to your mentoring then he's not doing his job and he's preventing you from doing an important part of yours. Keep in mind if you're boss feels like this dev isn't learning anything or listening to you and you haven't said anything to your boss then that reflects badly on you not the dev your mentoring.
Lastly if your company doesn't use GIT or PRs (pull requests) then that is a much bigger problem than the dev leaving comments in and you should be pushing to get the company to follow modern best practices that prevent problems like this or start running away and looking for a job that will be more beneficial to your career.