The 12-person jury found Chauvin, 45, guilty on all charges including second-degree murder, third-degree murder and second-degree manslaughter, concluding that the ex-cop's actions were a "substantial causal factor" in Floyd's death.
"I feel relieved today that I finally have the opportunity ... for hopefully getting some sleep," Philonise Floyd said during a Tuesday press conference after the verdict.
Floyd's brother said he "prayed" and had "faith" that Floyd would be "convicted," calling the past year "a long journey."
Philonise Floyd compared his brother to Emmett Till, a 14-year-old who was lynched in Mississippi in 1955, calling Till "the first George Floyd," but the difference today, he said, is technology.
"Today, you have cameras all around the world to see and show what happened to my brother," he said. "...I could do nothing but watch, especially in that courtroom over and over and over again, watching my brother get murdered."
Floyd’s brother Rodney Floyd said the family has been inundated with messages on social media and comments from strangers who approach them in public.
"This is everyone who’s been held down — pinned down — standing together in unity," he said, adding his brother is "smiling," and praised Floyd’s daughter, Gianna Floyd, who was present at the conference.
Members of Floyd's family who couldn't be at the trial watched and reacted to the verdict playing out live on TV, according to ABC News and ABC News 7.
"GUILTY! Painfully earned justice has finally arrived for George Floyd’s family," Floyd family attorney Ben Crump tweeted. "This verdict is a turning point in history and sends a clear message on the need for accountability of law enforcement. Justice for Black America is justice for all of America!"
He continued: "We still have work to do! We must pass George Floyd Justice in Policing Act to hold police accountable [and] prevent unjustified killings of marginalized POC."
Crump also posted a video of the family's post-verdict conversation with President Biden to Twitter:
Crump's firm, Ben Crump Law LLC, issued a separate statement Tuesday along with attorneys Antonio Romanucci, Justin Miller, Jeff Storms and other co-counsel, saying the verdict brought "painfully earned justcie" to Floyd and his family and goes "far beyond this city and has significant implications for the country and even the world."
"This case is a turning point in American history for accountability in law enforcement and sends a clear message we hope is heard clearly in every city and every state," the statement reads.
After Judge Peter Cahill announced the verdict, Philonise Floyd hugged prosecutor Jerry Blackwell, Attorney General Keith Ellison. Ellison and Blackwell shook hands.
Rodney Floyd told MSNBC that the Floyd family "broke down in tears" at the jury's decision, adding that "no family in history ever got this far."
"We were able to get a guilty charge on all counts. We got a chance to go to trial and we took it all the way. This right here is for everyone that's been in this situation," he said.
The former officer is expected to serve at least 40 years in prison.
A bystander video at the center of the trial depicted Chavin pinning Floyd to the ground with his knee on Floyd's neck for nearly nine minutes as onlookers yelled at the officer to stop.
As the case drawing to a close Tuesday, some stores were boarded up in Minneapolis in anticipation of protests and riots in the event that the final verdict ended up in Chauvin's favor.
Concrete barriers and razor wire were set up around the courthouse, and National Guard troops were on patrol. Floyd's death set off protests last spring in the city and across the U.S. that sometimes turned violent.
The city of Minneapolis on Friday agreed to pay $27 million to settle a civil lawsuit from Floyd’s family in March, which included $500,000 for the neighborhood where Floyd was arrested.
Floyd's brother Philonise Floyd said Tuesday that President Biden called him to offer support as closing arguments ended.
"He knows how it is to lose a family member, and he knows the process of what we're going through," Philonise Floyd said of Biden during an appearance on NBC's "Today" show. "He just let us know he was praying for us and hoping everything would come out to be OK."
While Philonise Floyd said he wanted protesters to remain "peaceful," he said he couldn't prevent people from expressing their pain – especially following the recent fatal police shooting of 20-year-old Daunte Wright just 10 miles from Floyd's encounter with Chauvin last May.
"It has been an emotional cinema picture, everyone watching around the world. We just want everybody to be peaceful, but at the same time I can't stop people from doing the things that they're doing because people are in pain, they're hurt," he said.
He added that "Daunte Wright was just killed 10 miles away from where we were in the courtroom," referencing a 20-year-old Black man from Brooklyn Center, Minnesota, who was killed on April 11 as police were conducting a traffic stop.
"We just want everybody to get it together and understand we can live with each other in unity. And we stand in solidarity with everybody across America," he said.
Philonise Floyd testified as a character witness during the trial earlier this month.
Fox News' Danielle Wallace and the Associated Press contributed to this report.