I also encountered this problem, when I tried to move an Android project from one computer to another. Since I have Android Studio 2.3 I don't have the option to run the standalone SDK-manager (or at least, I don't see any button).
On this website
http://m.blog.csdn.net/article/details?id=51204114
I found the solution to resolve the problem.
Go to Tools >> Android >> SDK-Manager >> SDK-Tools
Uncheck "Android SDK Platform-Tools" and press Apply to uninstall it again.
Then check it again to re-install it. Then I was able to compile my project again.