Moore, 26 joins from Championship side Cardiff City in a deal believed to be worth £500,000 - making him the Blades most expensive keeper ever, prior to that was Alan Kelly's £100,000 transfer from Preston in the early 1990's.
The keeper is expected to make his debut tomorrow at Millwall.
Blades boss Chris Wilder said: “There has to be competition for places. I’m here to make tough, strong decisions and to make us better as a group. Simon, we think, does that.”