Holliday, 64, had been missing for several days before his body was found in the creek near Preston Trails Golf Club in north Dallas.
The Dallas County Medical Examiner's office hasn't issued a cause of death, but Police Chief David Brown said Holliday may have slipped and fallen into the creek before drowning.
Holliday served on the force for 32 years before retiring.
"He served Dallas with distinction and with love," his family said in a statement. "Our family will always be grateful to the men and women who worked so hard to find Greg and bring him back to us."
"I never worked for a more ethical person than Greg," said retired Lt. David Payne.