The former Arsenal defender finalized his move on deadline night and will link up with his new teammates on Tuesday.
Manager Chris Wilder expressed his delight at bringing in an experienced defensive option after a busy transfer window.
Boss Chris Wilder said: "We've been light in the central defensive area ever since Harry Souttar's injury, so we're delighted to add Rob, a player who has played the game at the highest level for a number of years.
"It is the last remaining piece of the jigsaw and whilst we have had to wait until deadline day to get this one boxed off, I think our patience has been justified by getting Rob over the line.
"He's played in some huge games during his time with Arsenal, so he'll relish the situation he's walking into. He'll compete with the likes of Anel, Jack and others, and joins a squad which is looking far healthier than the one we had at the start of the window, as we look to attack the remaining part of the season."