The 24-year-old penned a two-year deal with Rovers on Thursday, bringing an end to his two-year association with the Bantams, where he made 59 appearances and scored 12 goals.
City boss Phil Parkinson said: "I had further chats with Dave since the end of the season but, like any player out of contract at this time of year, he had the option to also speak to other clubs as well.
"We made Dave an offer which we felt was a fair one but he has decided to go to Doncaster and we wish him all the best."
Syers added: "It was a tough decision to leave - I've had two great years at Bradford. I certainly wish them all the best for the future.
"The fans were absolutely tremendous to me from day one. I really hope the club can start rising back up the leagues."