Tyre Nichols' family is getting support from the one family that probably best understands their pain ... TMZ has learned George Floyd's loved ones will be at Tyre's funeral for a face-to-face meeting.

Famed civil rights attorney, Ben Crump is representing the Nichols family -- just as he did for George's -- and he tells us, several members of the Floyd family will be at the ceremony Wednesday in Memphis.

We're told the Floyds sent their condolences to Tyre's family after he was so badly beaten by Memphis police, he ended up in a hospital and died -- but the families have yet to meet in person.

That will change when they meet up at the Mississippi Boulevard Christian Church in Memphis for the funeral.

Meanwhile, Crump tells us Tyre's family has been invited to join ongoing efforts to get the George Floyd Justice in Policing Act passed by Congress ... and they're all on board.

We're told President Biden -- who spoke to Tyre's mom, RowVaughn Wells, and stepfather, Rodney Wells, Friday -- is trying to get Congress to turn its focus back on federal police reform legislation. He's invited Tyre's folks to be part of the push to get it signed into law.

A White House official tells TMZ ... the administration is sending 4 dignitaries to the funeral, including senior advisor, and former Atlanta mayor, Keisha Lance Bottoms.

Crump says Tyre's kin will schedule meetings with lawmakers and continue speaking out in favor of police reform -- 2 things the Floyd family's been doing since George was murdered by Minneapolis police.

The George Floyd Justice in Policing Act passed the House in 2021, but stalled in the Senate. Biden renewed his call to pass the act Friday -- after the Tyre arrest body cam was released -- and is urging Republicans in Congress to help Democrats pass police reform.