Blades boss Neil Warnock, who has been monitoring Kilgallon since the summer, has also sanctioned Paul Ifill's departure.
The former Millwall midfielder, who was rumoured to be interesting Leeds, has joined Crystal Palace in a £750k deal.
Kilgallon was a product of the Leeds United Academy and played 95 times for the Whites and also had a loan spell at West Ham.
The defender said: "This is a big opportunity for me in the Premiership. I'm here now and I'm really excited about it. I've played well in the Championship, but now this is a step up, so I have got to prove myself.
"I played a few games in the Premiership when I was younger and I did okay, but now I have to show what I can do all over again. I'm 23 today, and now I want to establish myself as a good, young defender in the Premiership. I want to do as well as I can."