Members of Smith's family could be heard crying in court as the verdict was read. Smith's death sparked days of unrest in Milwaukee.
Shortly after the verdict, Smith family attorney David Owens said they had filed a lawsuit against Heaggan-Brown and the city. The suit claims Milwaukee kept the former officer on the job despite a "pervasive pattern of excessive force and misconduct," including at least 16 "use of force" incidents.
Outside court, Smith's sister called for peace and his father, Patrick, said the verdict was "disrespectful."
"Why are they trained to kill when they're supposed to protect and serve us?" Patrick Smith said of police officers. "There is no justice here."
He added, "I want the community to calm down and come together."
Smith's sister Sherelle had a message for young people: "Don't give them a reason to take your life. Do something different in the community, try as hard as you can to be peaceful."
Milwaukee County District Attorney John Chisholm said he respected the jury's decision.
"We pursued it aggressively and we presented a strong case," he told reporters. "This is just an issue that this community had to decide. They made that decision."
Defense attorney Jonathan Smith said his client was "gratified" over the acquittal, CNN affiliate WISN-TV reported.
"Obviously, everyone recognizes there was a loss of life, and I don't think any officer would want to be put in that situation and to have to make those decisions that he did, but those decisions were made, and I think the jury properly evaluated them," Smith said.
Convictions rare in police shootings
The verdict comes at a time of increasingly strained relations between law enforcement officers and the communities they serve.
Heaggan-Brown was the third US law enforcement officer to be tried for shooting a black man in the last week. Convictions are rare.
On Friday, Minnesota police Officer Jeronimo Yanez was acquitted
of one count of second-degree manslaughter and two counts of intentional discharge of a firearm that endangers safety for the fatal shooting of Philando Castile during a traffic stop last year. In May, Tulsa police Officer Betty Shelby was acquitted
in the shooting death of Terence Crutcher, an unarmed black man.
In Cincinnati, a jury began deliberations Monday in the retrial of former University of Cincinnati police Officer Ray Tensing
in the fatal shooting of a motorist during a July 2015 traffic stop.
"The community relies on, depends and respects their law enforcement partners," Chisholm said.
"At the same time, they understand that this tremendous amount of discretionary power is given to police officers -- the power over life and death in certain circumstances -- and they want that to be accountable. But when they look at it closely they're looking at a circumstance which was fairly unique. ... You can't compare this to St. Paul. You can't compare it to Ferguson."
Milwaukee Police Chief Edward Flynn, in a statement via Twitter, said, "A year ago I told the public I'd seen nothing in the video that was a violation of the law or policy. The jury saw the same evidence and came to the same conclusion."
The prosecutor argued that Heaggan-Brown fatally shot Smith as the suspect attempted to surrender. But the former officer's attorney countered that his client made a split-second decision to protect his life and that of another officer.
The jury, which was sequestered, began deliberations on Tuesday -- less than a year after the shooting in northwest Milwaukee.
Heaggan-Brown, 25, faced 60 years in prison.
Body-camera video from another officer -- played for the jury last week -- showed that Heaggan-Brown shot a second bullet into Smith's chest after the suspect hurled his weapon over a fence and had his hands near his head. Smith was on the ground when he received the fatal shot.
The jury heard closing arguments Tuesday. They deliberated just under 10 hours over two days.
"Mr. Heaggan-Brown knew at the time he fired that second shot that Sylville Smith had already disarmed himself," Chisholm told the jury, WISN-TV reported.
"He knew that Sylville Smith was attempting to surrender."
But defense attorney Smith argued his client followed training and fired the second, fatal shot because he believed his life was in danger.
"The state admits that the first shot was a justified shot," the lawyer told the jury, according to the station.
"And our argument is that justification did not change over the course of 1.69 seconds between shots."
The defense rested Monday after calling its lone witness, Robert Willis, an expert in police use of force.
Willis testified that Heaggan-Brown acted in "accordance with his training," CNN affiliate WTMJ-TV reported.
His testimony centered on the 1.69 seconds separating the two shots. He testified the officer's decision to fire again was made before he even pulled the trigger. The second shot was justified, Willis told the jury, because officers are trained to assume a suspect may have more than one weapon.
Heaggan-Brown experienced the encounter in "real time," not in frame-by-frame motion as it was shown to the jury, Willis said, according to WTMJ.
"So when we see the trigger being pulled, we have to not consider that the moment of decision," he said. "It's not. We have to go back -- and I can't tell exactly how many frames but we have to go back two-tenths or three-tenths of a second -- we have to go back several frames ... to delve into the decision-making process that goes into firing this shot."
Willis, who wrote the use of force manual used by Milwaukee police officers, told the jury that Heaggan-Brown justifiably responded to a "deadly threat," WISN reported.
Last week, members of Sylville Smith's family gasped as body camera footage of the foot chase was played in court.
The reaction to the video, including sobs from Smith's family, caused the judge to clear the courtroom.
Officer fired over a different investigation
The shooting sparked days of unrest in the Sherman Park section of Milwaukee, a city long torn by racial tensions.
Prosecutors said his first shot was justified, but not the second, according to WISN.
Heaggan-Brown's former partner, Ndiva Malafa, testified last week they were chasing Smith, 23, because they saw he had a gun.
"I saw Mr. Smith exit the vehicle. I observed the firearm and at that point, we made eye contact. At that moment, I believe I started to -- I see him running northeast. Out of the corner of my eye, I see Heaggan-Brown chase him as well," Malafa testified, WITI reported.
Malafa's body camera footage was played several times in court, according to WTMJ. Malafa also guided the jury through the footage frame by frame, the station reported.
The video picks up as Malafa jumps out of this squad car. The shaky footage shows him trailing behind Heaggan-Brown, who is chasing Smith. The suspect ran across a lawn, turned a corner and headed toward a fence but slipped before reaching it.
Smith was armed with a Glock .40-caliber Model 22 semi-automatic handgun with an extended magazine containing 23 rounds.
An autopsy showed that Smith had a gunshot wound through his upper right arm and another to his right upper chest.
In the body camera audio, which was activated 30 seconds after the shooting, Heaggan-Brown was heard yelling at Smith: "Stop reaching." He moved Smith's hand away from his waist, the criminal complaint said.
Heaggan-Brown had previously said he believed Smith "was reaching for his waist so he discharged his weapon a second time."
The former officer still faces charges in an unrelated sexual assault investigation
. He has been fired from the police department.
In the separate case, a man told investigators that Heaggan-Brown sexually assaulted him while off duty two days after the shooting death of Smith.
The alleged sexual assault occurred on the morning of August 15 after a night of heavy drinking at a bar where the two men "sat and watched television as coverage of the Sherman Park protests [over Smith's death] aired," the criminal complaint said.