The officer, J Alexander Kueng, pleaded guilty in October to a single state count of aiding and abetting manslaughter.
He appeared in Hennepin County District Court on Friday through a video link from a federal prison in Ohio, where he is serving up to three-and-a-half years on federal charges stemming from Floyd's death.
Kueng, who will serve both sentences concurrently, was given credit for 84 days already served.
He was one of four officers who were called to a Minneapolis grocery store on May 25, 2020, and tried to take Floyd into custody on suspicion that he used a fake $US20 bill to buy cigarettes.
During the encounter, the senior officer on the scene, Derek Chauvin, pinned the handcuffed Floyd's neck to the ground with a knee for more than nine minutes, causing his death.
Kueng, 29, and fellow officer Thomas Lane helped Chauvin restrain Floyd, while another officer, Tou Thao, kept bystanders from approaching the scene.
Kueng's sentencing represented a taste of justice for the Floyd family, civil rights lawyer Ben Crump said.
"While the family faces yet another holiday season without George, we hope that moments like these continue to bring them a measure of peace, knowing that George's death was not in vain," Crump said.
Kueng's lawyer, Thomas Plunkett, sought to deflect some blame from Kueng, saying his client was a rookie on his third day on the job at the time of the incident.
Chauvin was convicted of murder in a state trial and sentenced to 22-and-a-half years. He also pleaded guilty to federal charges and is serving a federal sentence of 21 years concurrently.
The three other officers were convicted in federal court of depriving Floyd of his civil rights and sentenced in July to between two-and-a-half to three-and-a-half-years in prison.
