The Millers have paid an undisclosed fee for the 22-year-old who made 21 appearances for Celtic in three years.
Playing mainly as a right-back, Fisher began his career at Farnborough before moving to the Glasgow club in 2013.
He made 23 appearances while on loan at St Johnstone last season, as they finished fourth in the Premiership.
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Championship side Rotherham United have signed defender Darnell Fisher on a three-year deal from reigning Scottish Premiership champions Celtic.