In this context (sexual harassment), there's no such thing as employee privacy, i.e., the person who came to you "in confidence" can't have expectations of privacy. The LAW requires that you take certain steps once you know about something like this.
If you have an HR person/dept, definitely forward the matter to them. They should know what to do (investigate, analyze and make a decision). The "bad" actor may not lose his job. It depends on a number of things like how have you handled these complaints in the past if, God forbid, this isn't your first complaint, what's the guy's history as to these things (has he done anything like this in the past), etc.?
If you don't have HR folks, then refer the matter to your in-house attorney. If you don't have that, then you'll probably want to reach out to an employment law counsel, who can help walk you thru the steps (including an investigation that is documented).
By the way, you're going to need to adopt a strong anti-harassment policy to put into your employee handbook. Make sure everyone gets the policy, has training on the policy and, of course, be sure to enforce it going forward.
Good luck. Feel free to contact me if you have any questions (jimfalvey (at) yahoo (dot) com).