The service caps off six days of mourning for the black man whose death inspired a global reckoning over police brutality and racial injustice.
Mr Floyd, 46, was to be laid to rest next to his mother in the suburb of Pearland. He cried out for his mother as a white Minneapolis police officer pressed a knee on his neck on May 25.
About 6,000 people attended a public memorial on Monday in Houston, where Mr Floyd grew up.
Under a blazing Texas sun, mourners wearing T-shirts with his picture or “I Can’t Breathe” – the words he uttered as he lay pinned to the pavement for what prosecutors say was eight minutes, 46 seconds – waited for hours to pay their respects. Mr Floyd’s body lay in an open gold-coloured casket.
Mr Floyd’s death sparked international protests and scattered violence and drew new attention to the treatment of African Americans in the US by police and the criminal justice system.
In the past two weeks, sweeping and previously unthinkable things have taken place: Confederate statues have been toppled, and many cities are debating overhauling, dismantling or cutting funding for police departments. Authorities in some places have barred police from using chokeholds or are otherwise rethinking policies on the use of force.
Mr Floyd’s death has also reshaped the US presidential race.
To be re-elected, President Donald Trump must bounce back from one of the lowest points of his presidency, with recent polls showing that eight in 10 Americans believe the country is heading in the wrong direction and even spiralling out of control.
Meanwhile, former vice president Joe Biden, the Democratic candidate for president, met with Mr Floyd’s family on Monday, according to a photo posted on Twitter by the civil rights leader the Reverend Al Sharpton. Mr Biden planned to provide a video message for Mr Floyd’s funeral.
Over the past six days, memorials for Mr Floyd were held in Minneapolis, where he lived in recent years, and Raeford, North Carolina, near where he was born.
The memorials have drawn the families of other black victims whose names have become part of the debate over race – among them Eric Garner, Michael Brown, Ahmaud Arbery and Trayvon Martin.
Across the US, Mr Floyd’s death set off days of mostly peaceful demonstrations along with bursts of arson, assaults and raids on businesses, with more than 10,000 people arrested. But protests in recent days have been overwhelmingly peaceful.
Four Minneapolis officers were arrested in Mr Floyd’s death, which was captured on mobile phone video by bystanders. Derek Chauvin, 44, was charged with second-degree murder. J Alexander Kueng, Thomas Lane and Tou Thao were charged with aiding and abetting. All four could get up to 40 years in prison.