Left-back Spurr has joined on a two-year deal after failing to agree a new contract with Doncaster, while midfielder Cairney arrives from Blackburn on a six-month loan deal.
Rovers manager Gary Bowyer said of Spurr: "First and foremost, we are delighted that Tommy has agreed to join us, as there were several clubs chasing his signature.
"We have done our homework. He is a good lad and he will add extra height and energy to our back line.
"He has had a good upbringing in terms of where he learned his trade, in the Championship and League One, so he knows the demands of what is required at this level.
"He played every game for Doncaster last season and that mentality, of winning football matches and winning promotion, is something we are trying to get more of into our dressing room."
Scotland U21 international Cairney, meanwhile, has signed until January and will be eligible for the Capital One Cup.
And Sky Sports understands that Blackburn are close to agreeing a deal to sign Hull City midfielder Corry Evans.