The US director, known for films such as The Last Picture Show and Paper Moon, died of natural causes on Thursday 6 January at his home in Los Angeles, his daughter Antonia Bogdanovich said.
Multi-award winning actress Dern said Bogdanovich “taught me so much” and gave her a first great acting opportunity.
Posting a photo to Instagram of the set of the 1985 film Mask, she wrote: “Another hero lost.
“My teacher and guide, who gave me my first great acting opportunity. My friend through life, who taught me so much about filmmaking.
“I love you, Peter, with everything.”
Pop star Cher, who also starred in Mask, said the director had discovered “amazingly talented artists” throughout his career.
“Just heard Peter has died,” she tweeted.
“I’m proud of the film (mask) we made together, & in the end I’m sure he must have been as well. He made some very memorable films and discovered amazingly talented artists.”
Fellow singer and actress Streisand, who starred in his 1972 screwball comedy What’s Up, Doc?, added: “Peter always made me laugh!
“He’ll keep making them laugh up there too. May he rest in peace.”
Bogdanovich was born in Kingston, New York, in 1939, and started out as a film journalist and critic before moving on to film-making.
His well-known films include The Last Picture Show in 1971, which earned eight Oscar nominations, and Paper Moon in 1973.
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The Big Lebowski star Jeff Bridges said Bogdanovich had left behind the gift of “his incredible films and insights”.
“My heart is broken – my dear friend Peter is no longer with us in the physical form,” the actor tweeted.
“I loved him and will miss him. What a wonderful artist. He’s left us with the gift of his incredible films and his insights on the filmmakers he so admired. I love you Peter.”
The official account of late US musician Tom Petty posted a lengthy tribute to Bogdanovich on Twitter, describing the director as “a close and personal friend” of the artist.
Sharing a picture of the two together, the account said: “We are sad to hear of his passing.
“Tom was so thrilled when he agreed to be the director for what would become the film about his legacy with the Heartbreakers – Running Down A Dream.
“Peter remained a close friend of the family until he passed away last night and we will always be grateful that he was a part of our lives and the legacy of Tom Petty and the Heartbreakers.
“God bless Peter Bogdanovich.”
Former Family Fortunes host Les Dennis added: “Peter Bogdanovich was a master filmmaker and a true lover of Cinema. RIP.”
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