The Fuller House star was found dead in a hotel room in Orlando, Florida, on Sunday. He was 65.
"Just wanted you guys to know that Bob Saget was one of the nicest men on the planet," Davidson wrote. "When I was younger and several times throughout our friendship he helped me get through some rough mental health stuff. He stayed on the phone with my mom for hours trying to help in anyway he can -- connecting us with doctors and new things we can try. He would check in on me and make sure I was okay."
He concluded his post with a message to his late friend, "I love you Bob it was an honor to know you. Thank you for your kindness and friendship. My condolences to the family."
Davidson has long been open about his struggles with mental health. He previously revealed that he was diagnosed with borderline personality disorder (BPD) at the age of 23. He's also spoken about mental health on SNL as well as at events and during interviews.
Saget died on Sunday in his hotel room at the Ritz-Carlton in Orlando, Florida, the Orange County Sheriff's Office confirmed. A cause of death has not been released at this time.
"We are devastated to confirm that our beloved Bob passed away today," Saget's family said in a statement to ET. "He was everything to us and we want you to know how much he loved his fans, performing live and bringing people from all walks of life together with laughter."
Saget is survived by his wife, Kelly Rizzo, and his three daughters, Aubrey, Jennifer and Lara, who he shares with his first wife, Sherri Kramer.