Besides the USD 5M indie movie, Moon (2009), you can also add stuff like 2001, Wall-E, The Matrix, etc. to the list of inspirations for the USD 120M Oblivion production. But I agree that the similarity with Moon is striking. The fact that Moon was released only recently doesn't help.
In interviews, Joseph Kosinski makes it a point to mention that he wrote the script eight years ago (which would date it to 2005). Moon's script (which has its own set of inspirations) is dated to 2007. In this interview he brushes aside similarities to Wall-E and states the following:
It actually isn’t. It’s surprisingly… Tron had fifteen or sixteen hundred visual effects shots in it and Oblivion is eight hundred shots, so it’s almost half. Because I was able to do so much in camera. Hopefully it feels like a big movie, which is what I always wanted to do, but we did it… You never get credit for it publicly, but doing movies at a reasonable price compared to the other summer blockbuster films is something that I’m very proud of. We really did this for… It’s an original property. It’s not based on anything known, so you have to stretch it as far as you can. That’s something I’m really happy with.
So there you have it. There is no formal connection between the two properties.