The 21-year-old is set to partner fellow defender Matt Redmile for Shrews boss Kevin Ratcliffe's side this weekend.
Artell has failed to make an appearance this season for The Merry Millers season and will look to help the Gay Meadow side push up the table from their current position of seventeenth place.
On the signing of Artell, Ratcliffe told the Shropshire Star: "He played about 30 games in Rotherham's promotion-winning side so he's got plenty of League experience for a young player.
"I'm going to ask him to defend, that's what he's here to do. I want him to win the ball with his head and cut through it with his feet.
"I think we've got enough experience here at the moment so I wanted someone who was raw.
"We've been letting in far too many goals and that has concerned me all season, so hopefully David coming here will put a stop to that."
