Bolger, 26, would have been out of contract at Highbury in the summer.
The Irishman, who joined Fleetwood on a free transfer from Southend United in the summer of 2016, was offered a new Town contract last summer but turned it down.
He had been a first-team regular under both Uwe Rosler and John Sheridan but has fallen out of favour since the arrival of head coach Joey Barton last summer.
He was Town’s player of the year for 2016/17, when they reached the play-offs, and made a total of 121 appearances for the club, scoring 13 goals.
Scottish club Hibernian reportedly offered a six-figure sum and Championship club Hull City were also rumoured to be circling.
Bolger said he had offers from a higher level but was excited by the Lincoln project.
Imps boss Cowley said: “He (Cian) only had six months left on his contract, so we have been able to take him for free, which we are really pleased about.”
And the Imps boss spoke about his shock at Bolger’s availability.
He added: “I’m delighted to have him with us. He’s done fantastically well at Fleetwood. He was one of the best centre-halves in League One last season.
“It was a surprise to us that he was made available. Last summer he had interest in Hull City and Millwall, and Fleetwood turned down half a million pounds for him from a Scottish club.”