The 20-year-old Irishman joins the Trotters for an undisclosed free and although he will train with the first-team squad, he will initially play with their development side.
"Delighted to have signed for BWFC," tweeted Bolger, who is a product of the Leicester City academy and was named academy player of the year in 2009.
Dougie Freedman said: "Although he'll train with the first team squad, Cian is one who will initially play in the development squad.
"We believe that he has the potential to be knocking on the door for a regular place in the senior team in the near future."
Bolger had three different loan spells with Bristol Rovers over the past 18 months, making 52 appearances and scoring two goals.
Rovers failed with a bid earlier this month, and that alerted several Championship clubs, including Bolton, to his availability.