It's a goby of some kind, definitely. Put him in a QT tank and give him some time to let him settle down if you need a more specific ID. However, if you don't think he can eat anything in your tank, I'd suggest putting him into your display unless he'll eat frozen foods. Most sifter gobies need old, dirty sand to stay healthy, and he does look to have a sifter goby mouth.
With the possible exception of little shrimp, yes, gobies are reef safe. In fact, sometimes a reef isn't goby safe; don't put anything with a strong sting down near the bottom, as he might be stung.