This is an old puzzle that comes from Plato's dialogue Euthyphro: if something is wrong simply because God says so, then morality sounds a little arbitrary. For example, what if God said murder was good?--would that make it good? (please don't say yes psycho). On the other hand, if something is good for independent reasons, independent from God's will, then morality sounds like it's...well, independent of God, which is presumably bad for religion (so some people think). Thus I'm in a pickle. For God fearing philosophers like me, I want both. I want morality to be connected to God in some way, but not in a way that leaves out tons of people.
Jeremy Bentham, the atheist Utilitarian philosopher, thought that morality rests upon an independent principle "apart" from God so to speak. That independent principle was this: good is maximizing happiness and minimizing pain. That's it. But he left room for God. He said that if God exists, then God would operate under this principle:
"The dictates of religion would coincide, in all cases, with those of utility, were the Being, who is the object of religion, universally supposed to be as benevolent as he is supposed to be wise and powerful...Unhappily, however, neither of these is the case...there seem to be but few...who are real believers in his benevolence...if they did, they would recognize that the dictates of religion could be neither more nor less than the dictates of utility: not a tittle different" (125).
In other words, God would be the best embodiment of utilitarian morality. However, people would not have to go through God (or the Bible) to get to morality. Anyone with half a brain can figure it out.
Kant, on the other hand, did believe in God, but he too thought that morality must not depend on God's will or the Bible, but instead on God's Reason (that is, reason, or rational thinking). Why? Because nobody really knows what God's will is; people disagree and that causes a lot problems. Morality, Kant says, must be reasonable, accessible to all, and quite simple: only act on those principles which can be universalized to all. Through this principle we get to the Golden Rule - never treat people as a means but as ends-in-themselves - and we get many of the 10 commandments.
My opinion is in line with Kant. I do think that morals "come from God" simply because everything comes from God, by definition. But how do people access morality? That's the question. Where do we actually get it? What or who is the gatekeeper? Our parents? Yeah sure sometimes. Religion? Yeah, many times. But where does religion get it from? Like Kant, I think Reason (our minds) ought to the be ultimate judge of what's right and wrong. In the same way that human beings come from evolution and God, morality comes from Reason and God.
Of course empathy is a huge natural component as well. Empathy, when found in a compassionate, rational, and open-minded person - that's a beautiful thing.