Frid, who created the role of vampire Barnabas Collins in the 1960s gothic soap opera, died last week, but his death wasn't announced to the media until Thursday.
Depp plays Collins in Tim Burton's soon-to-be-released movie version of "Dark Shadows," for which Frid filmed a cameo appearance.
"Jonathan Frid was the reason I used to run home from school to watch 'Dark Shadows,'" Depp said in a statement to People.com. "His elegance and grace was an inspiration then and will continue to remain one forever more. When I had the honor to finally meet him, as he so generously passed the torch of Barnabas to me, he was as elegant and magical as I had always imagined. My deepest condolences to his family and friends. The world has lost a true original."
Frid's nephew, Don, told CNN the 87-year-old actor died early April 14 in Hamilton, Ontario. He had been battling pneumonia, and was hospitalized for about two weeks before he died, CNN said.