He is the first New Jersey State Police trooper killed in Iraq.
Kelly, who spoke Arabic, was working to restore local government and services in the former Shiite militia stronghold.
The 48-year-old was on his third deployment to Iraq.
Kelley was assigned to the State Police counterterrorism unit in Hamilton, and also worked with the terrorism task force in Newark.
He was divorced with two children.
Kelley joined the state police in 1988.
"He touched many lives throughout the law enforcement and military communities, and he will be deeply missed by us all," said Col. Joseph R. Fuentes, state police superintendent.
As part of his counterterrorism efforts, Kelley interviewed detainees at Guantanamo Bay, Fuentes said.
Kelley's honors included the Essex County 200 Club Award for Valor, he said.
Iraqi officials suspected the bombing was an inside job, and suspicion fell on the headquarters' Shiite guard force. The blast was the second deadly attack to strike Americans promoting municipal governments in as many days.
The attack comes as U.S. military and civilian officials step up efforts to take advantage of a sharp drop in violence to promote the local administration and restore services in Sadr City and other areas.
The increased presence of the Americans in local communities has made them more vulnerable to attacks. But U.S. commanders believe that's key to a strategy that has helped drive down the levels of violence to the lowest point in more than four years.
