Ferguson, 64, of Miami, was found guilty of killing six residents during a home invasion robbery in Carol City, 12 miles north of Miami, The Miami Herald reported Tuesday.
He was also convicted in a separate case of slaying teenagers Belinda Worley and Brian Glenfeldt in January 1978.
In its ruling Monday, the Florida Supreme Court upheld the decision of a Miami-Dade County judge who rejected Ferguson's legal claims on grounds they were filed too late.
His attorneys were appealing chiefly on the grounds that he is mentally ill and his execution would constitute cruel and unusual punishment.
On Tuesday and Wednesday, Ferguson's lawyers are expected to present evidence of his mental health to a judge in Bradford County, where his execution is scheduled to take place.
Gov. Rick Scott's office has set an execution date of Oct. 16.