To be honest you're actually in a pretty good position here, unless he's already in a relationship or whatever, you can pretty much expect that he'll say yes if you do ask him out (provided you're a reasonably charming young lady). The question then becomes in how you go about it - and really this will pretty much send out a first impression of who he thinks you are as a person.
You could try and do it more slowly (do the classic liking of one of his old instagram posts or whatever), but really you might drag on to the point where he finds it annoying and just wants you to go away (which obviously you dont want). Fortunately, as you've already made eye contact and done all that stuff, the most natural thing to do is to just walk up to him and talk (you dont have to ask him out or anything but just talk about whatever you feel like). Leave a lot of it to him of course as you'll probably be quite shy and generally you might want to know more about him then he might immediatly about you. From here you just have to be a bit gusto and take the initiative if you can. He knows that you approach first (which is rare) so he knows you're into him, therefore there's no point waiting for weeks to hang out. A good way of doing this though is to meet up with him with your friends (the opposite scenario can be intimidating) and then after it's just upto you.
Really you haven't got anything much to lose.