The 43-year-old, who retired in 2017 after defeating Conor McGregor, will cover all the costs of the service after Floyd was killed by a Minneapolis policeman last week.
The news came from Leonard Ellerbe, the chief executive of Mayweather Promotions, who was speaking to ESPN on Monday.
The death of Floyd has caused an eruption of protests across the world, with violence breaking out in parts of the United States between police officers and protestors.
Floyd Mayweather Jr
Image credit: Getty Images
The police officer responsible for Floyd's death, Derek Chauvin, has been charged with third-degree murder and second-degree manslaughter.
Ellerbe confirmed that Floyd's family had accepted Mayweather's offer, highlighting that the former five-weight world champion has done this type of thing a number of times in the past.
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"He'll probably get mad at me for saying that, but yes, (Mayweather) is definitely paying for the funeral," Ellerbe said.
"Mayweather has done these kind of things over the last 20 years," added Ellerbe, saying that the reason that it was he telling people was because Mayweather himself didn't want to talk about the gesture.
There will be a memorial service for Floyd on Thursday in Minneapolis, followed by a similar service in North Carolina (where Floyd was born) on Sunday.
The funeral itself will be held on June 9 in Houston, Texas.