When discussing it with my students, we concluded that the ending was "more hopeful than happy." Whether it was satisfying depends heavily on what the reader expects out the novel's end.
If we look at it simply in terms of conflict resolution, then the ending is satisfying. Assef is eliminated as a threat, and Sohrab is in America. Amir learns the truth about his family, and finally does right by Hassan.
This question made me think for a while. For me, the conclusion was only somewhat satisfying but I think it had more to do with the context in which I was reading the book. At the time, Afghanistan was a powder key about to erupt but we were in Iraq. I had not known much about Afghanistan before reading this book, and when I finished it I was thinking about what was going to happen in Afghanistan next. I think the book personalized it for me. I now had characters in my head.
I personally believe that the conclusion to this excellent story is definitely satisfying. The reason for this is that it gives us a seed of hope for a better future for Sohrab. Some might criticise the ending for the way that it is not a traditional "happy ending," and yet, given the experiences that Sohrab has been forced to endure, the realists among us have to acknowledge that such trauma is not going to be reversed in a short period of time. Note how the narrator himself responds to the smile that symbolises such hope:
It was only a smile, nothing more. It didn't make everything all right. It didn't make anything all right. Only a smile. A tiny thing. A leaf in the woods, shaking in the wake of a startled bird's flight.
But I'll take it. With open arms. Because when spring comes, it melts the snow one flake at a time, and maybe I just witnessed the first flake melting.
We are not given the complete happy ending that perhaps we would like, but what we are given is a sign of hope that this happy ending is there at some point in the future. The narrator is very realistic about this smile and what it represents, admitting that it doesn't suddenly sweep away all the abuse that Sohrab has suffered, but his comparison to this smile being like the first snowflake melting in spring clearly indicates that this could represent a beginning.
Personally, therefore, I think the conclusion is very satisfying, because it does not present us with an unrealistic happy ending. It is clear from the ending that Sohrab has a long journey to complete on his voyage towards recovery, but we are permitted to see the first step of that journey, which is a real privilege, and foreshadows that journey's completion.
I think you can defend both sides of this question. One can say that the conclusion is not satisfying because Hassan is no longer alive, and Amir is never able to make amends to his friend while is his alive. When the two are young Amir commits the sin of watching his friend, Hassan, get raped in the alley, and he does not do anything to stop it. Amir then frames Hassan and tries to make Baba turn his back on Hassan. Amir lives with this guilt for most of his life. Even after moving to American, the guilt eats away at Amir. Since Amir never speaks to his friend, and he is never able to make amends while Hassan is alive, one can argue that the end of the book does not satisfy the crime that was committed when the boys were young.
However, a more popular answer to this question may be that the book ends with a satisfying conclusion. Amir receives a call from an old friend in Kabul and learns that there is "a way to be good again." Amir learns that Hassan has died, but before he died he had a son. Amir returns to Kabul to get Hassan's son, and he brings him back to America to have a better life. The book ends with Amir and Hassan's son flying kites in America. This activity of kite flying is similar to what Amir and Hassan did as boys prior to the sin in the alley. At the end of the book, Amir looks at Hassan's son's smile and he is reminded of his friend. One can argue that the conclusion allows Amir to obtain redemption for his past sins because he is now taking care of Hassan's son and therefore doing right by his old friend.