Blackburn have strengthened their attack ahead of the forthcoming campaign by signing DJ Campbell on a two-year deal.
The experienced forward makes a quick return to Ewood Park, after his three-month loan spell with Rovers at the end of last term.
Blackburn boss Gary Bowyer was delighted to land the 31-year-old on a free transfer following his release from Queens Park Rangers.
"He's a player who has huge experience and is a proven goalscorer at this level," Bowyer said.
"He feels he has some unfinished business with the club and is hungry to succeed.
"He will add a different dimension to our attacking options and he is the right character we want to have on board."
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."
It was already established Phil Neville is to become a member of Moyes' backroom team but now Giggs will work alongside his former team-mate, having already agreed a one-year contract extension last term.
"It's a great privilege to be appointed a player coach. I hope I will be able to bring my experience to bear, having been both a player and part of the Manchester United family for so long," said Giggs.
Often linked with the United manager's job at some point in the future, Giggs has been taking his coaching badges and is due to attain the UEFA Pro Licence next summer.
"It's no secret that I have been taking my qualifications and I see this as
the first step in my future career,'' said Giggs.
"I'm really looking forward to working alongside David and the team.''
Having confirmed Steve Round, Chris Woods and Jimmy Lumsden were following him from Everton, concern had been expressed about the lack of United experience in David Moyes' backroom team following his appointment as Sir Alex Ferguson's successor.
Neville's arrival at the Aon Training Complex this morning went some way to allaying those concerns.
However, the decision to appoint Giggs is a masterstroke.
The Welshman won a record 13th Premier League title last term and was part of all but the first two of Ferguson's major triumphs.
He will be an invaluable aid to Moyes as he learns the ropes, with the Scot due to face the media alongside skipper Nemanja Vidic on Friday.
"I am delighted that Ryan has accepted the chance to become player coach,'' said Moyes. "His success and ability to adapt his game over a number of years gives him an unrivalled perspective on the modern game.
"His career is an example to any aspiring young player and I'm sure that both he and the players will benefit from his new role.''
