The tribute began in the staff sergeant's hometown of Simi Valley with a slow drive down First Street, where hundreds of people lined the curb.
Later at a 9:30 a.m. mass, Cullins's fellow officers and Marines carried his body into the Cathedral of Our Lady of the Angels in downtown Los Angeles.
Outside, the ladders of two fire trucks crossed to form an arch with a U.S. flag draped beneath them.
"There's no greater compliment that I can pay to an individual than to say that he or she was a champion of heroes, and that's what Josh was," LAPD Chief Charlie Beck said.
Cullins is the second LAPD officer killed in Afghanistan this year. He was serving with the Marine Reserves as an explosive ordinance disposal officer.
"I've learned that bravery is doing something you're scared to death of," said Duane McCoy, who spoke for Cullin's father at the mass. "My son was the bravest man I know."
After services, an LAPD honor line saluted their fallen comrade. A somber score from a bagpipe filled the hall as four Marines and four LAPD officers carried Cullins's casket out of the cathedral.
The tribute to Cullins wasn't limited to just the church.
The northbound lanes of the 101 freeway were reserved solely for the officer for a short time in the afternoon. Dozens of vehicles followed him for the last time.
On Tuesday, friends and family attended a public viewing.