There have been some very good answers in this tread, but I felt it might be good to approach this subject from a different angle.
Do atheists all around the world share the same set of morals?
No. I think you will find that no two people, atheist or not, share the exact same set of morals. Everyone is different to a larger or lesser degree, even if they grew up together.
If not, what is the source of morality then?
And here comes the meat of the reply.
Depending on who you ask you will get many different answers. Some will point to their parents teaching them right from wrong. Others will attribute their morals to the specific culture they are a part of. And some will claim that they get their morals from their religion. And while all of these may have some influence on the individual person, and perhaps even on groups of people, this still doesnt answer the question. Not really.
The thing that has puzzled anthropologists for decades is that even in vastly different cultures there seems to be several overlapping basic type morals. As it turns out almost all societies share a disregard for things like murder, theft, rape and other serious crimes. Why is that? Surely if morality was down to cultural biases we would see some divergence here. Instead we see an almost global consensus that certain things are just not done, and are in fact frowned upon.
Now, it would be very unscientific of me to attribute this to some kind of deity, and in any case people believe in such a varying spectrum of gods that surely even a religious person must see that this cannot be the reason. The answer is a very simple one. The answer is Evolution. At least Evolution of a kind.
Imagine, if you will, a society in which murder, theft and rape was accepted, or even seen as a suitable way of life. Imagine the death toll, the insecurity, the instability. The chaos. How long do you think such a society would survive? Not for very long, Im sure. The math is quite simple in this one and fairly obvious even to elementary school children. (Dont scrub elementary school children though. They understand more than most people think...). Therefore it follows that only those societies that rejected this kind of behaviour would survive and thrive. And that, simple as it may sound, is the reason for this seeming universality in our morals.
But hang on a second... Surely, if this pattern is correct then we would see these results among other social animals as well. And we do! Altruistic behaviour among higher primates is well documented, not only towards their own species, but even towards their caretakers (and in some cases, random humans they encounter), whom they probably see as flock mates anyway. But this is not a huge surprise. After all, we have more in common with the great apes than we do not. It would be expected that we also share some behavioural traits.
Very well then. I give you the South American Vampire Bat. Of these species of bat (there exists at least three) all of them display a particular type of altruistic behaviour. See, vampire bats (or bats in general for that matter) have a very high metabolism to the point that going a few nights without feeding can actually be fatal to these amazing critters. So when they go out hunting for the night some will be lucky enough to find some animal to feed from, and some unlucky few will not. So how do they get around this dilemma? Shouldnt we be seeing bats starving to death left and right? No. Not if they share the spoils. These bats have amazingly developed a sort of social security network, not unlike those found in most industrialized countries. When a bat finds himself on hard times, he can usually rely on his flock mates to provide for him by regurgitating some of the blood they got a hold of. The assumption, of course, is that he will, should the need arise, repay the favour. And in this manner the bats set themselves up to survive even if they themselves are having trouble finding food. In addition to this we find that among all social mammals there seems to be a barrier towards killing their own kind, at least within their own flock and family. They usually also have a ranking system and clearly defined rules of ownership, be it with regards to breeding rights, hunting grounds or the sharing of food.
Now, one might argue that most, if not all the bats in a particular flock are cousins and closely related, and thus one might postulate some kind of kin-selection as the basis (not to be confused with group-selection). And if we transfer this argument to our own societies it seems we might have a hard time explaining how altruistic behaviour persists even in societies in which we are not related to the majority of the people we meet. But what we have to remember is that this is a fairly recent development. 10.000 years ago (the blink of an eye in evolutionary time) most humans lived in small societies where they were probably related to many of the people there, and in any case, we were likely to deal with these people on a daily basis. Hence what we recognize as altruistic behaviour would have made perfect sense.
And it still does. The evolution of societies has shown us that cultures that adhere to certain moral codes and who display altruistic behaviour have staying power. They are safer, more ordered, and, not to mention, a lot more pleasant to live in. In other words, having certain common moral denominators is necessary to have a functioning society, and a society that does not have them will suffer because of it, and may not survive the test of time.