The baby, who is "healthy and feisty", was born at the Breach Candy Hospital on Wednesday morning.
"I would like to thank all my well wishers and fans," Rani said in a statement issued by Aditya's production banner Yash Raj Films.
"Today life has given us god's greatest gift with Adira. We thank fans our friends and well-wishers for their unconditional support and blessings. With joy we begin this new chapter in our lives," she added.
Rani and Aditya, who had for long been in a relationship, had entered wedlock in April 2014 in Italy. They are both accomplished in their fields of acting and filmmaking in Bollywood.
Their friends and family members are excited about the news.
Rani Mukerji and Aditya Chopra become proud parents to a baby girl named 'Adira'.
— Yash Raj Films (@yrf) December 9, 2015
Aditya's younger brother Uday announced on Twitter: "IT'S A GIRL!!!!!"; while the couple's close friend and filmmaker Karan Johar shared: "Am an uncle to a beautiful baby girl today!!!!! @udaychopra !!! Rani and Adi had a baby girl!!"
IT'S A GIRL!!!!!
— Uday Chopra (@udaychopra) December 9, 2015
Am an uncle to a beautiful baby girl today!!!!! @udaychopra !!! Rani and Adi had a baby girl!!
— Karan Johar (@karanjohar) December 9, 2015
Rani and Aditya Chopra become proud parents to a baby girl named Adira. Congratulations!
— rishi kapoor (@chintskap) December 9, 2015
ITS A GIRL !!!! So so excited baby Adira is born !! #Adi #Rani
— Parineeti Chopra (@ParineetiChopra) December 9, 2015
Actress Parineeti Chopra also shared her joy by posting: "IT'S A GIRL !!!! So so excited baby Adira is born !! #Adi #Rani"; and veteran actor Rishi Kapoor said: "Rani and Aditya Chopra become proud parents to a baby girl named Adira. Congratulations!"