The Fulham goalkeeper spent last season on loan at the Millers.
The Millers will host Wigan in the League Cup opener.
The Millers will need to make some improvements if they are to compete in the Championship.
The former club-record signing was released by Paul Warne at the end of the season.
The Millers boss wants Richie Towell, Josh Emmanuel and Marek Rodak back at the AESSEAL New York Stadium.
What Millers connections will be in Russia for the next month?
The Irish midfielder is heading back to Brighton for pre-season training.
The draw will be made in Vietnam on Friday.
Stubbs was in charge of the Millers from June 2016 to October 2016.
The left-back is the latest youngster to pen contracts at the club.