BRUNSWICK, Ga. — A jury on Tuesday determined that the three white Georgia men who murdered Ahmaud Arbery violated a federal hate-crime statute by depriving Mr. Arbery, a 25-year-old Black man, of his right to use a public street because of the color of his skin.

The jury also found the three men — Travis McMichael, 36, his father, Gregory McMichael, 66, and their neighbor William Bryan, 52 — guilty of attempted kidnapping and found the McMichaels guilty of one count each of brandishing or discharging a firearm during a violent crime.

The men now face up to life in prison for the federal crimes, on top of the life sentences they received earlier this year in state court after being convicted of Mr. Arbery’s murder, with only Mr. Bryan eligible for parole. The federal convictions ensure that the defendants will receive significant prison time even if their state convictions are overturned or their sentences reduced on appeal.

The victory will also be important, symbolically and emotionally, for Mr. Arbery’s family, as well as other observers who believed that the pursuit and fatal shooting of Mr. Arbery on a Sunday afternoon in February 2020 amounted to what the Rev. Al Sharpton called “a lynching in the 21st Century.”

During the federal trial, lawyers for the three defendants argued that the men had not been motivated by racial animus, but rather because Mr. Arbery seemed to them like a potential crime suspect. Prosecutors, however, presented copious evidence that showed that the men harbored coarse racist views about Black people.

After a graphic video of his fatal shooting went viral in 2020, Mr. Arbery joined a grim list of African American victims of recent violence that has triggered a broader conversation about the treatment of Black people at the hands of law enforcement and in everyday situations. This week’s verdict offered another example of the judicial system’s varied responses to these incidents, coming 10 months after a jury found Derek Chauvin, a white former Minneapolis police officer, guilty of murdering a Black man, George Floyd, and a few days after another white former police officer, Kimberly Potter, was sentenced to two years in prison for shooting Daunte Wright, a Black motorist, at a traffic stop.

Social justice advocates were generally pleased with the outcome of Mr. Chauvin’s trial, but some have expressed frustration that the sentence given to Ms. Potter, who was found guilty of manslaughter, seemed too lenient.

The Georgia hate-crimes trial followed a dramatic murder trial in state court concerning the Arbery killing. Key aspects of that trial were televised and the case attracted scores of demonstrators, including well-known Black activists like Mr. Sharpton and the Rev. Jesse Jackson, to the small coastal city of Brunswick. A large group of activists chanted and cheered outside the Glynn County courthouse on the day before Thanksgiving, when a nearly all-white jury issued the guilty verdicts.

In the murder case, prosecutors treaded lightly on the topics of race and racism, focusing instead on the rash and dangerous decisions the men made when they decided to jump into a pair of trucks and chase the unarmed Mr. Arbery, who was on foot, through their quiet South Georgia neighborhood.

Even before the federal trial began, it was expected to be different because the men’s racist views — evidence of which was divulged or hinted at in pre-trial state hearings and court filings — would take center stage, with jurors forced to determine whether racism had been a motive in the actions of the defendants that day.

In January, the McMichaels appeared to be heading off the possibility of going through a federal trial, having reached plea deals with the U.S. Department of Justice in which they would have been sentenced to 30-year sentences to run concurrent with their state sentences. However, Mr. Arbery’s parents came to court and pleaded for U.S. District Judge Lisa Godbey Wood to reject the deals, in part because they would have allowed the men to spend the bulk of their sentences in the federal prison system, which is generally thought to be a less harsh environment than the Georgia state system. Judge Wood ended up rejecting the pleas.

When the evidence of the defendants’ racism was finally laid out in court, it proved to be both voluminous and harsh, including numerous uses of racist epithets and racial insults. Along with video of Mr. Arbery gasping for his final breaths on the pavement and testimony that the defendants did not render aid to him, the government’s case seemed to take an emotional toll on jurors, some of whom could be seen crying. Last week, one of the jurors asked court officials if counseling was available.

Even the defense lawyers acknowledged to the jury — made up of eight white members, three Black members and a Hispanic member — that their clients’ views were reprehensible. J. Pete Theodocion, a lawyer for Mr. Bryan, referred to racism as “among the lowest of human emotions.”

Text messages recovered from Mr. Bryan’s cellphone showed that he opposed his daughter’s relationship with a Black man, using a racist slur to describe the boyfriend in a text exchange four days before Mr. Arbery’s killing. A witness said Gregory McMichael made disparaging comments about a Black tenant who rented from him and about the civil rights leader Julian Bond.

Travis McMichael, the man who used his Remington shotgun to fatally shoot Mr. Arbery three times at close range, was revealed to have repeatedly used racist slurs, and expressed the desire to see violence and death visited upon Black people.

The government introduced no evidence to show that the men directed their racist language toward Mr. Arbery specifically. But prosecutors noted that some of the racist language had been used a few days or months before the killing. They also seemed to bet on the jury being revolted by how much evidence of racism there was, with the quantity of insults showing that these were more than accidental slips of the tongue.

“At the end of the day, the evidence in this case will prove that if Ahmaud Arbery had been white, he would have gone for a jog, checked out a house under construction and been home in time for Sunday supper,” Bobbi Bernstein, a Justice Department lawyer, told the jury. “Instead he went out for a jog, and he ended up running for his life. Instead he ended up bleeding to death, alone and scared, in the middle of the street.”

Gregory McMichael’s lawyer, A.J. Balbo, told the jury that Mr. McMichael had not been out to hunt down a Black person that day, but rather to go after Mr. Arbery specifically, after a police officer showed security camera images of Mr. Arbery entering a nearby house that was under construction.

Mr. Arbery had entered the house numerous times in the weeks before the shooting, including the moments before the chase began, though there is no evidence he stole or disturbed the property inside. Twelve days before the shooting, Travis McMichael had also seen Mr. Arbery outside the house and had called 911, claiming he saw Mr. Arbery reach toward his waistband, a gesture, Mr. McMichael said, that made it seem like he could have been reaching for a gun.

Travis McMichael’s lawyer, Amy Lee Copeland, noted that her client had been shocked, rather than “gleeful” after the shooting, which occurred after Mr. Arbery, pinned in by the two trucks, clashed with the younger Mr. McMichael, who had by that point stepped out of his truck with his shotgun in his hands.

Mr. Theodocion noted that his client, Mr. Bryan, did not know anything about Mr. Arbery’s history with the McMichaels, or his visits to the house, when he saw Mr. Arbery run by his house, with the McMichaels in full pursuit. Mr. Bryan joined the chase assuming that Mr. Arbery had done something wrong enough to warrant the pursuit, Mr. Balbo said.

The death of Mr. Arbery was met with revulsion from both conservative and liberal lawmakers in Georgia. It prompted state legislators to significantly weaken a citizen’s arrest law that one local prosecutor had cited soon after the shooting to argue that the three men should not be arrested. It also prompted them to pass a state hate-crime law.

This month, the legislature also passed a resolution declaring Wednesday, the two-year anniversary of the killing, “Ahmaud Arbery Day.”