"It's a little disappointing for us, we offered him a good deal to make him the clubs second highest earner, we tried our best to keep him but he has opted to move to Shrewsbury," said boss Ronnie Moore to the clubs official site.
"Ian has been a good servant to the club and we wish him all the bets for the future."
Sharps leaves the Millers after a four year stay after signing from Tranmere in 2006.