Priyanka, who depicted the boxer's life story in a recent biopic, said having portrayed her on screen, she understood the hard work and sacrifices that Kom went through for the game.
"I feel almost as if I have won... What an achievement, what a role model! She has proved yet again that she is unstoppable.
This amazing mother of three has made India proud today just as she has done throughout her career and has shown the world what a true champion is made of. I am privileged and proud to have been able to tell this amazing woman's story to the world," Priyanka told PTI.
The film's director Omung Kumar also congratulated Kom.
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Bachchan tweeted, "Mary Kom wins gold. What a feat... Proud Indian!"
Actor Farhan Akhtar, who played Milka Singh in another sports biopic, tweeted, "Congratulations to Mary Kom on her gold medal win. Reach For The Sky."
Shabana Azmi said Kom was an inspiration to all women who want to dream big.
"Congratulations Mary Kom. You do us proud! More power to you. You are an inspiration to women who want families and follow their dreams," she said.
"Heartiest congratulations to Gold Medalist Mary Kom for an amazing performance in Asian Games 2014," wrote actor-politician Shatrughan Sinha.
"Hail Mary Kom!!! What an incredible lady! Proud Indian. Gold Medal," actress Dia Mirza tweeted.
Kom, 31, defeated Kazakhstan's Zhaina Shekerbekova in the flyweight (51KG) summit clash in Incheon, South Korea to become the first Indian woman boxer to clinch a gold medal in the Asian Games.