The 27-year-old initially signed a short-term deal after he was released by Preston at the end of last season.
But after a recent string of impressive performances the Wales international has been handed a new deal.
Morgan has been almost ever-present since his switch from Deepdale, making 14 appearances for the Millers so far this term.
"When I first signed my ultimate goal was to stay long-term so I am delighted that it has progressed so quickly into a more permanent situation," he said via a club statement.
"In terms of settling in here, I have loved it. The lads are great in the dressing room, I am enjoying coming into work, it has been like a breath of fresh air for me to play again."