Kelly left the Royals in the summer and had been without a club, but has spent a period on trial with the Millers, and clearly impressed manager Neil Redfearn.
United have struggled defensively since the start of the campaign. The club conceded five against Ipswich Town prior to the international break.
Redfearn believes adding the 32-year-old, who has been capped 38 times by the Republic of Ireland in a career that has seen him play Premier League football for Tottenham Hotspur, Birmingham City and Fulham, will shore up his defence.
He said: “Stephen is a vastly experienced defender. He can play across the back four. His position is probably right-back, but he can play at centre-half.
“He’s experienced at international level, played nearly 50 times for the Republic of Ireland.
“He’s a good singing, because he brings experience at a time when we need it to start keeping clean sheets.”
Redfearn also revealed that the club were able to snatch him ahead of other interested teams from the Championship.
He continued: “We’re fortunate in that there’s been two or three players who are out of contract that have interested a few clubs that we’ve been able to get to first.
“He impressed me from day one. His attitude and how he applies himself has been infectious on other players.
“When good players come in they make a difference.”