Brown and green eyes are like a layer of pigment over blue eyes. That pigment is dominant over just plain ol' blue, so with both of you having that pigment there is theoretically a strong chance of her having green or brown eyes.
[what I say from this point on is a simplified (and probably quite messy) explanation of complicated science. It should be close enough to not be wrong, but any real scientist would slap me for how I explain it].
Eye colour is a bit of a lottery though because there are multiple genes in play. You might have brown eyes because you have a single brown and a bunch of blue genes. In that case the dominant brown would appear because it sits on top of all those blue. Your partner may have green for the same reason.
You don't pass on all your genes when making a baby though. Each sperm packs a bag with whatever genes they can carry and that only includes some eye genes. Those some are added to the egg's some and makes your baby's whole.
So, if you did have that pile of blue each, both the sperm and egg involved could have decided to only take blue. In that case, there would be no brown or green to sit on them so your little girl would end up having blue eyes.
If either of you give a brown or green gene though, your little girl should end up with some shade of brown or green. Since you both have brown or green (and thus at least one lot of brown/ green pigment), there should be a stronger chance of any children you have getting the genes needed for brown or green eyes. It only takes one of you passing on that gene so the two of you having it gives basically double odds.
So yeah basically after all that, it's still a total mystery and you'll have to wait until she's born to find out. So try to avoid giving her a name based on her eye colour until you see her.
Congratulations btw