Miller, 24 completes a move to Bramall Lane after weeks of speculation for a fee in the region of £70,000 - he had a year remaining on his Crewe contract and could make his debut in next Tuesday's friendly match at Rotherham United.
Alex Assistant-Manager Neil Backer told This is Staffordshire; "It's a good move for him, and I think the time is right because he wasn't a regular in the team and some of our younger players have gone past him, but we wish him all the best. He is one of our own who has done very well for this club."
He made his Crewe debut in November 2006 in a4-0 FA Cup defeat at Bradford City and has since made 122 (+57) appearances and scored 43 goals in all competitions before joining the Blades, he was absent from the team which secured promotion in the Play-Off Final last May.