I've been on the other side of this situation with my now-husband. We didn't talk about our finances in detail until we’d been together for a couple years and started seriously planning to get married.
You’re probably aware (but just in case, and for the benefit of other readers), that US student loan debt is... really not great. It can’t be discharged in bankruptcy and there are very limited situations in which you might have some of it forgiven. With the amount you mentioned, you're probably looking at sizable monthly payments, which will impact your budgeting, savings rate, and ability to qualify for other loans (e.g. a mortgage).
So, two main questions to think about first:
- What is your plan for paying off your loans?
- What have you and BF talked about as a plan for your future together? Is what you've discussed actually viable, given your debt?
When you feel prepared, let him know you want to talk. Depending on your relationship, you might tell him the topic beforehand, or just ask him to set aside some time. This will help set the stage that it's a serious conversation and ensure you have plenty of time to discuss if needed.
Since you’ll undoubtedly revisit the topic of budgeting in your relationship, I’d suggest keeping this initial conversation focused on simply laying out your situation. Explain your plan, show that you’re taking this seriously and being responsible. You don’t need to get into the nitty-gritty of exact numbers if you’re not comfortable with that, but at least saying what you’ve said here - six figures - is probably descriptive enough for your purposes at this stage. (Don’t be too vague, though! My SO only said at first that it was “a lot”, and I was a bit shocked finding out later just how “a lot” it was, because I had never been in so much debt myself. If your boyfriend didn't go to college, he may not be aware of what "a lot" of student loans can be, either.)
Then, listen. He might be disappointed or sad, he might want to share something about his own finances, he might roll up his sleeves and help you make a budget. This really depends on his personality and how disruptive this news is to any joint future plans you have, so I can only advise you to be patient and calm with answering questions he might have. Either way, it will likely be a learning experience for both of you - and financial compatibility is extremely important for long-term relationships, so that's a good thing!
(Personally, I reacted with all of the above -- obviously it wasn’t a dealbreaker, but it was a bit of a rude awakening. I had been imagining and daydreaming about how we would get married and buy a cute little house together in 3-5 years, so I was pretty disappointed when I found out that wasn’t going to happen. So it’s great that you’re having this conversation now, so you can set realistic expectations.)
Given that your goal is just to let him know about your debt, and that you aren't currently financially entangled, I wouldn't advise asking him to reveal his financial situation during this conversation. If he volunteers, that's one thing, but it could come off very poorly (prying or even opportunistic) to inquire during this same conversation. Instead, save that for another time when he feels ready to share his side too.