The 22-year-old has been on trial at the Millers for the last week and after impressing boss Steve Evans, he has earned a three-year deal at the New York Stadium.
Newell played in Saturday's 2-1 friendly win over Mainz, after which Evans revealed he had a quandary over whether or not to offer the player a deal.
The Scot came down on the side of yes and Newell is now primed to be the first-choice left-back for Saturday's season-opener against MK Dons.
“This young man has considerable experience in the Championship for one being so young and is comfortable in any position on the left hand side of the pitch, and indeed centrally," Evans said.
"Last season he was outstanding and I am led to believe he swept the boards for every Peterborough United player of the year award that was on offer.
“We have signed another young player to add to those already recruited and for me they blend fantastically well with the experienced lads we have brought together.
“I would like to acknowledge both chairman Darragh MacAnthony and director of football Barry Fry for handling this in the professional manner they have done.”
Peterborough boss Dave Robertson added: "It is a great opportunity for Joe and I am sure he will do very well in the Championship with Rotherham."
