Hennepin County District Judge Peter Cahill's ruling was dated Wednesday and made public on Thursday.
Mr Cahill said there is enough probable cause for the second-degree murder charge and manslaughter charge against Derek Chauvin to proceed to trial.
He also denied defence requests to dismiss the aiding and abetting counts against three other former officers, Thomas Lane, J Kueng and Tou Thao.
"In this court's view, with one exception, the state has met its burden of showing probable cause that warrants proceeding to trial against each of these Defendants on each of the criminal charges the state has filed against them," Mr Cahill wrote.
He said it will be up to a jury to decide whether the officers are guilty.
Mr Floyd, a black man who was in handcuffs, died on May 25 after Chauvin, who is white, pressed his knee against his neck as Mr Floyd said he could not breathe and became motionless.
His death sparked protests in Minneapolis and beyond.
Prosecutors argued there was probable cause for the officers to go to trial on all of the charges, saying Chauvin intentionally assaulted Mr Floyd, which is an element of the second-degree murder charge, and that the other officers assisted.
During the entire time Mr Floyd was pinned to the ground "the officers remained in the same position - Chauvin knelt on Floyd's neck, Kueng and Lane remained atop Floyd's back and legs, and Thao continued to prevent the crowd of concerned citizens from interceding", prosecutors said.
The officers ignored Mr Floyd's pleas to stop, cries from the concerned crowd and their own training, prosecutors said.
Defence lawyers argued there was not enough probable cause to charge the former officers.
Chauvin's lawyer said his client had no intent to assault or kill Mr Floyd, while lawyers for the other officers argued their clients did not intend or conspire to help Chauvin.
Defence lawyers said Mr Floyd's drug use was a factor in his death.
The county medical examiner classified Mr Floyd's death as a homicide, with his heart stopping while he was restrained by police and his neck compressed.
A summary report listed fentanyl intoxication and recent methamphetamine use under "other significant conditions" but not under cause of death.
Reporting by PA