This is a tough one. It's hard to "stop" your feelings when they are going off like they are right now, especially when it certainly seems like she's reciprocating. It was a good sign that she says her other relationship is ending, and all signs are positive if she wasn't in a relationship already, but you need to be a little cautious about this. She's not completely out of that relationship, and even when she is she could end up realizing she still has feelings for the other guy and wants to go back to him, and you'll get burned. Additionally, you don't want to become the shoulder to cry on. Or the person she vents to when he makes her angry. Or the guy she turns to when she doesn't get the kind of attention she should be getting from her current bf. It's very easy for that to happen in the scenario you're in right now.
I've been in this type of situation twice, actually. First time it ended HORRIBLY. I stayed in contact with the girl for a few YEARS while she was in the process of breaking up with her current boyfriend. It was pathetic - every month she'd come up with another reason why she couldn't call it off - I am busy with school this month, we are going to a wedding this month, I think I want to give it a fair shot and try to fix it for my family blah blah blah. We hung out as if we were bf/gf, but she was still with the other guy, no end in sight for when she'd end it with him. And she complained about him all the time. How she was unhappy, how she needed to end it, how we were so much better together. I hung around for way too long and ended up getting hurt. She actually did end up breaking up with the guy, but by that time I had come to my senses and moved on.
Second time (yes, I got myself into this situation a second time) was with my current gf. She was breaking up with her live-in boyfriend when I met her and assured me it was all said and done, she just needed to find an apartment and move out. The difference here is that she had a date when she was moving out, and it was about 2 months in the future. I told myself to not get too close until she moved out and "officially" called it off. We remained friends, talked with regular frequency, never got physical (even though there were clear signs from both of us that we wanted to), and waited until she moved out. She moved out by the date she said, broke up with him in the process, and started seeing me. We've been together for about a year and a half now and things couldn't be better. Was it a rebound relationship - maybe. Did she jump from one relationship to another - well, sorta. She was checked out of the other relationship for a few months before we met, so in her mind she had already moved on months before I even met her.
So, my advice to you would be to take things slowly until she is officially done with her boyfriend. Hopefully you'll be able to pull out some info about when that time will be, but I wouldn't get into a relationship with her (even if it's not physical) until she's out of her other one first. Only she will know if she's ready to start something with you right after she ends it with her current bf, but just because she's seeing someone now doesn't mean you can't start seeing her right after she ends it with the current guy. Just make sure you don't get strung along, and don't jump headfirst into this and start acting like she was your gf until she's done-done with that other relationship.