Moore was struck in the head; the other officer was uninjured.
Flags at city and state of New York government buildings will be flown at half-staff in memory of Moore until his interment Friday.
"Officer Moore put his life on the line in order to protect his fellow New Yorkers, and our state is a better place because of him," Gov. Andrew Cuomo said in a statement. "Like so many of his brothers and sisters in uniform, Officer Moore served with selflessness and courage, and he will be greatly missed. Our thoughts and prayers are with his family."
His wake will be Thursday at Frank J. Chapey and Sons Funeral Home in Bethpage on Long Island, and the funeral will be Friday at St. James Roman Catholic Church in Seaford.
JetBlue said it was offering free airfare to law enforcement officers attending Moore's funeral.
The New York Mets will honor Moore with a moment of silence at Tuesday night's game against the Baltimore Orioles, CNN affiliate WCBS-TV reported.
And the team will wear NYPD caps during batting practice.
Mayor Bill de Blasio and Police Commissioner Bill Bratton announced Moore's death
"In his very brief career -- less than five years -- he had already proved himself to be an exceptional young officer," Bratton said. "In that career, he had made over 159 arrests protecting and serving the citizens of this city."
Moore had received two exceptional police service medals.
"We don't give them out easily," Bratton said. "He worked for them; he earned them."
In a statement, Patrolmen's Benevolent Association President Patrick Lynch called Moore "another brave police officer who placed his life between crime and the good people of the city."
"Brian Moore is a hero in every sense of the word. His loss is felt by all of his brother and sister officers as we pray for Brian and for the loving family that he left behind. His family now becomes our family and we will support them in every way possible through the next difficult days and beyond."
Moore was the son, nephew and cousin of New York police officers, CNN affiliate WABC-TV reported
. On Monday, silence enveloped the entrance of Jamaica Hospital in Queens during the departure of a New York Police Department ambulance carrying his body. A line of officers stood in salute.
At the 105th Precinct, children arrived with their parents Monday night to pay their respects, WABC-TV reported. Outside, residents left flowers and lit candles.
The man accused of the shooting, Demetrius Blackwell, was arrested and charged with first-degree attempted murder. Bratton said Queens District Attorney Richard Brown told him he would go before a grand jury to upgrade the charges.
The suspect is related to former New York Giants and Cleveland Browns player Kory Blackwell.
"I was devastated to learn of my cousin's alleged involvement in the shooting of police officer Brian Moore, and there are no words strong enough to convey my sorrow over what has cast a devastating shadow over many lives," Kory Blackwell said in a statement. "The Blackwell family does not and never has condoned violence in any form. For years, our family tried to help Demetrius lead a more productive and law-abiding life. My heart goes out to the family for their tragic loss."
Being with the New York Police Department was Moore's dream, de Blasio said.
"He did everything a good police officer was supposed to do," he said.
Moore had proved himself courageous, the mayor added.
Blackwell, 35, appeared before a judge Sunday and did not enter a plea.
What happened this past weekend
Moore and another officer, Erik Jansen, 30, were sitting in an unmarked police vehicle in Queens on Saturday when they saw a passerby adjusting something in his waistband, according to the NYPD.
Moore, who was driving, pulled up behind the man, later identified as Blackwell, to ask about it. Blackwell allegedly pulled a gun from his waistband and opened fire on both officers, who were in the car and had no chance to fire back.
NYPD Chief of Detectives Robert Boyce said Moore's partner was able to identify Blackwell after he was arrested.
Two witnesses also identified Blackwell as the man they saw running with a firearm in the street near the site of the shooting, Boyce said.
The suspect was arrested nearby as he tried to retreat into the backyards of neighborhood homes, he said.
On Monday, police recovered a gun -- a Taurus Model 85 5-shot revolver -- from one of the backyards near where Blackwell was apprehended, Boyce said.
The gun had three spent rounds and two live rounds. It was one of 11 firearms that were stolen in Perry, Georgia, in 2011, Boyce said.
Ten of those guns have been recovered in the years since -- nine of them in New York, he said.
Blackwell's attorney, David Bart, told CNN that it wasn't unusual for no plea to be entered at this stage, saying that in "a case like this, the court rarely asks for one at this time."
"I don't think anyone should rush to judgment," Bart said. "I'm still working and looking into things."
If convicted, Blackwell faces 15 years to life in prison.
Two New York City police officers, Rafael Ramos and Wenjian Liu, were shot and killed in an ambush in Brooklyn days before Christmas.