The 23-year-old, who is a Scotland youth international, has joined the Millers on a two-year contract with the option of a third after passing a medical earlier this week.
"Young Michael Tidser is a player that we are delighted to have recruited given the options he has had since the end of the season," Red Devils boss Steve Evans said.
"He is young, has a great pedigree and is now ready to establish himself back at a higher level of football.
"My head of recruitment, Paul Raynor and myself have all watched the lad in action since the turn of the year and he has been in sparkling form.
"Again I must thank Tony Stewart and Paul Douglas, who worked tirelessly over the weekend to ensure that young Tids became a Miller.
"He is a superb passer of the ball, he's always inventive and creative with his passing and is sure to be an asset to the squad we have in place."
Tidser becomes the Millers' seventh summer signing as they prepare for life back in League One and Evans has turned his attention to a striker.
He added: "In respect of the squad, my sole focus is now in the strikers department, and we are working towards a conclusion on that which in turn gives us an excellent squad for the challenges that League One will present."