Lori De Waal, his representative, says Farina died Monday morning in a Scottsdale, Ariz., hospital after suffering a blood clot in his lung.
Farina, originally from Chicago, got the Commitment to Chicago tribute in 2012 at the Chicago Film Critics annual awards.
Farina insisted his 2011 film "The Last Rites of Joe May" be shot in Chicago.
The film was the main event at the 2011 Chicago International Film Festival. At the time, Farina told ABC7's Janet Davies that he's thrilled with his career.
"I believe I'm the luckiest guy in the world, and I wake up and thank God for everything that's happening, you know, I don't take anything for granted," Farina said.
Born Feb. 29, 1944, in Chicago, he was a city police officer before turning to acting in his late 30s.
Chicago's top cop, Supt. Garry McCarthy, said Farina was on the department 18 years, never forgot where he came from and always saluted the men and women in blue in Chicago.
"While he was cherished by audiences around the world, he will always be first and foremost a guy from the Near North Side who helped make this city safer," McCarthy said in a statement. "We respect him for his service, we regard him for his talent, and we will remember him always."
One of his first roles was at the Steppenwolf Theater in Chicago, where he played a Vietnam veteran in a play called "Tracers." He was a Vietnam veteran himself.
Farina appeared in films including "Get Shorty," ''Saving Private Ryan" and "Midnight Run." Farina's first film was the 1981 action drama "Thief," directed by Michael Mann, who Farina met through a mutual friend while still working for the Chicago Police Department.
Among his many TV portrayals was Det. Joe Fontana on "Law & Order." He starred in the 1980s cult favorite, "Crime Story" and most recently was in the HBO drama series "Luck."
"'The Last Rites of Joe May' represents the best of Chicago filmmaking, featuring outstanding Chicago actors, led by a commanding, nuanced performance from Dennis Farina, and steeped in colorful characters and the neighborhood flavor of the city," said Mimi Plauche, the Chicago International Film Festival's Head of Programming.
Said director, Joe Maggio, "Before I even made my first film, I remember thinking of all the great filmmakers who had premiered at the Chicago Film Festival, and dreamed of showing a film there. Now to be selected as the opening night film - it's a tremendous honor. It's especially gratifying to be returning to Chicago, a city that showed us so much generosity during production and really made the whole film possible."
Farina is survived by three sons, six grandchildren and his longtime partner, Marianne Cahill.
Farina's family is asking that instead of flowers, donations be made to the 100 Club of Chicago. www.100clubchicago.org
The Associated Press contributed to this report.