One month after the Full House star was found dead on Jan. 9 at the Ritz-Carlton in Orlando, Florida, his family confirmed in a statement to PEOPLE that he died due to head trauma.

"The authorities have determined that Bob passed from head trauma," the Saget family said on Wednesday. 

"They have concluded that he accidentally hit the back of his head on something, thought nothing of it and went to sleep. No drugs or alcohol were involved."

Saget's family added that they've been "overwhelmed with the incredible outpouring of love from Bob's fans" in the weeks since his death, and that the support has "been a great comfort to us and for which we are eternally grateful."

"Now that we have the final conclusions from the authorities' investigation, we felt it only proper that the fans hear those conclusions directly from us," they continued. 

"As we continue to mourn together, we ask everyone to remember the love and laughter that Bob brought to this world, and the lessons he taught us all: to be kind to everyone, to let the people you love know you love them, and to face difficult times with hugs and laughter."

Saget is survived by his wife Kelly Rizzo and his three daughters — Aubrey, 34, Lara, 32, and Jennifer, 29 — whom he shared with ex-wife Sherri Kramer.

When Saget's autopsy was completed on Jan. 10, authorities had said there was "no evidence of drug use or foul play."