Kher, 62, said he was "deeply humbled and honoured" to be appointed chairman of the "iconic FTII".
"I will perform my duties to the best of my abilities," he said in a tweet.
Kher, a graduate from Delhi's National School of Drama (NSD) who has appeared in over 500 films and many plays, was conferred the Padma Shri in 2004 and the Padma Bhushan in 2016 for his contribution in the field of cinema and arts.
Kher's wife Kirron Kher, the BJP MP from Chandigarh, was amongst the first to congratulate him.
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"Congratulations my dear @AnupamPkher for becoming FTII Chairman! Know you will do a great job!," she said on Twitter.
Born on March 7, 1955, in Shimla, Kher completed his education from the D A V School in the city.
He has previously held the post of chairman of the Central Board of Film Certification and director of NSD.
Then just 28, Kher played the role of a retired middle class man grappling with his son's death.
After "Saaransh", he went on to star opposite many big Bollywood celebrities, including Anil Kapoor, Shah Rukh Khan, Salman Khan and Akshay Kumar, sometimes as the villain, the comic relief or the friendly father.
In 2002, he attempted to become director with "Om Jai Jagadish" but the film was not a success.
Kher has also written and starred in a play about his own life called "Kucch Bhi Ho Sakta Hai", which was directed by Feroz Abbas Khan.
Kher's colleagues and contemporaries congratulated the actor on his new appointment.
"Excellent change. @AnupamPkher finally replaces Gajendra Chauhan or whatever his name is as FTII Chairman. Finally, the government is listening to us!," said journalist-adman-filmmaker Pritish Nandy.
"Welcome step! After @prasoonjoshi_ @AnupamPkher!! Moving in the right direction... Thank you for this @smritiirani," he said.
"Congratulations Shri @AnupamPkher ji, for being appointed as @FTIIOfficial chairman," said actor-politician Paresh Rawal.
Director Madhur Bhandarkar tweeted, "Heartiest congratulations to @Anupamkher sir for being appointed as the Chairman of FTII.
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