On Friday, a prosecutor said Bourdain had no traces of drugs or alcohol in his system.
The famous chef had several tattoos, getting his first at 44.
Bourdain told Maxim in August 2017 that each tattoo marks a significant moment in his life.
"I don't overly place importance on them, but [tattoos] do commemorate in a way that photographs can't," Bourdain said. "I stopped taking photographs a long time ago when I travel. There's this realization that the lens is inadequate to capture the moment, so maybe I'm just looking to mark time in another way that's very personal."
Gladys Bourdain said that a private ceremony will be held soon, adding, "He would want as little fuss as possible."
A Bourdain family spokesperson told the BBC the family has no plans for a public memorial at this time.