The Yash Raj Films's project which is the third installment in the franchise, also stars Katrina Kaif, Abhishek Bachchan and Uday Chopra.
Aamir plays a suave thief in the movie.
"It is spellbinding! Yes... Just out of 'Dhoom 3'. Still searching for the right words to describe it. 'Dhoom 3' is spectacular," tweeted Amitabh Bachchan on his son Abhishek's film.
"Go Dhoom -more power to you," said Riteish Deshmukh.
Filmmaker Kunal Kohli, who saw the premiere show, said he will watch the movie again today.
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Choreographer-director Farah Khan wished luck to Abhishek, who will also be seen in her upcoming movie 'Happy New Year'.
"Congrats and all the best Abhishek for your release today."
Abhishek himself took to Twitter and said, "Ladies and Gentlemen, today is Dhoom Day.