Garrone also has won the best director award for the movie by the European Film Academy.
Looking ahead, "Gomorra" is considered Italy's best hope for the Best Foreign Language Film award at the Academy Awards.
At the European Film Awards, Kristin Scott Thomas won best actress for her role in "I've Loved You So Long," while Toni Servillo won best actor in two movies, "Gomorra" and "Il Divo" by director Paolo Sorrentino.
Garrone's film is based on a best-selling book by Roberto Saviano, denouncing the Naples-based Camorra crime syndicate's hold on everything from fashion to waste disposal.
In accepting the best film award, Garrone said he regretted that Saviano could not attend the Copenhagen ceremony because he lives in hiding in fear he could be slain.
"I want to thank everyone who has participated in this dangerous movie," Garrone said.
The movie also grabbed the award for best screenplay.
British actress Dame Judi Dench was honored by the European Film Academy with a lifetime achievement award.
"I am completely overwhelmed," a visibly moved Dench said after receiving a standing ovation.
Singer Marianne Faithfull handed over similar awards to the Danish director quartet that conceived the filmmaking principles known as Dogma in the mid-1990s.
Lars von Trier, Soeren Kragh-Jacobsen, Thomas Vinterberg and Kristian Levring stripped props and lighting. The Dogma rules also forbade sound editing and any equipment other than hand-held cameras.
British director David Yates received the People's Choice Awards for "Harry Potter and The Order of the Phoenix," a recognition given by European moviegoers.
The annual event, held this year in the Danish capital, celebrated the continent's film industry as a European counterweight to the Academy Awards.
The audience included Crown Prince Frederik, his Australian-born wife, Crown Princess Mary, and Danish Prime Minister Anders Fogh Rasmussen.