Judge Peter Cahill said he will attach a 22-page memorandum to the sentencing order on his judgement.
Judge Cahill said he did not base his sentence on emotion or public opinion but instead the application of the law to specific facts.
Speaking to the court on Friday, Judge Cahill said: “I am not going to attempt to be profound or clever because it’s not the appropriate time.”
The 270-month sentence is a 10-year addition to the presumptive sentence of 150 months.
The judge said the decision was based on Chauvin’s abuse within a position of authority and also “the particular cruelty shown to George Floyd.”
To the Floyd family, the judge added: “You have our sympathies and I acknowledge and hear the pain that you are feeling.”
In an emotional impact statement on Friday during the sentencing, Terrence Floyd, George Floyd’s Brother questioned why Chauvin stayed on Floyd’s neck for so long.
He added: "I am here on behalf of me and my family. We seek the maximum penalty.
"We don’t want to see no more slaps on the wrists for me and my community.”
Gianna Floyd, George Floyd’s 7-year-old daughter, said in a message to her father: “I miss you and I love you.”
Philonise Floyd, brother of Floyd, said: “I haven’t had a real nice sleep due to the nightmares I’ve constantly had from the death of my brother.
“For an entire year I had to relive George being tortured to death."
"Chauvin had no regard for human life- George’s life.”
Mr Floyd’s nephew Brandon said he will be "forever traumatised" by what happened.
Chauvin was found guilty in April of murder and manslaughter.
Chauvin has been held in solitary confinement at a state prison at Oak Park Heights.
Three other ex-police officers who helped detain Floyd are due to go on trial in March 2022.
The sentence comes after the judge rejected former Minneapolis police Officer Derek Chauvin's request for a new trial over the murder of George Floyd hours before the sentencing.
Judge Peter Cahill denied the request on Friday, saying that defence attorney Eric Nelson had not shown that Chauvin was denied the right to a fair trial.
Chauvin was convicted of second-degree unintentional murder, third-degree murder and second-degree manslaughter for pressing his knee against Floyd's neck for about 9 1/2 minutes as George Floyd said he could not breathe and went limp.
Bystander video of Floyd's arrest for suspicion of passing a counterfeit 20 US dollar bill prompted protests around the world and a nationwide reckoning on race and police brutality.
Prosecutors asked for 30 years, saying Chauvin's actions were egregious and "shocked the nation's conscience."
Defence attorney Eric Nelson requested probation, saying Chauvin was the product of a "broken" system and "believed he was doing his job".
Cahill found that aggravating factors in Floyd's death warrant going higher than the 12 1/2-year sentence recommended by the state's sentencing guidelines.
The judge found Chauvin abused his position of authority, treated Floyd with particular cruelty, and that the crime was seen by several children. He also wrote that Chauvin knew the restraint of Floyd was dangerous.