The actor married his partner Louise last year and has a one-year-old daughter.
“We’re absolutely heartbroken to announce that Finnian passed away after a sudden decline in his condition,” the statement continued.
“You were the greatest husband, father, son, brother and friend we could ask for.”
The family thanked people for their support and kind words during this “really difficult time”.
His Hope Street co-star, Cameron Cuffe, said he had “brought joy to so many”.
Eddie Doyle, Head of Content Commissioning, BBC Northern Ireland, said Finnian was a “key part of Hope Street’s appeal”.
“He brought so much to his character PC Ryan Power over the last three series.
“Our thoughts are with his wife and daughter, family and friends and the cast and crew of Hope Street at this time.”
In a statement Long Story TV described him as a “much-loved member of the Hope Street family”.
“He was an absolute joy to work with and he brought a great sense of fun to set everyday and was popular with audiences as PC Ryan Power.
“We send our deepest sympathies to his wife, his daughter and his wider family and friends.
“He will be missed in Port Devine and by all his friends at Long Story TV.”