The 35-year-old star shared his excitement on Twitter and thanked fans for their blessings. The baby was born yesterday.
"She has arrived and words fall short to express our happiness. Thank you for all your wishes," he wrote.
Many Bollywood celebrities congratulated the new parents.
"I am really happy for them and will like to congratulate Shahid and Mira for the new addition in their family," Jacqueline told PTI.
Director Karan Johar congratulated the actor and Mira for their newest arrival in the family on Twitter.
"Huge congratulations to @shahidkapoor and Mira... Nothing more precious than a baby girl... Lots of love...," he tweeted.
Shahid's "Udta Punjab" co-star Alia Bhatt took to Twitter to wish them joy.
"Congratulationssssssss to the most amazing couple @shahidkapoor @MiraRajput !!!!! Can't wait to see this beautiful baby girl!!!!," she wrote.
Anushka Sharma also gave her love to the baby girl on the micro-blogging site.
"Congratulations to both of you and lots of love and good health for the baby girl!!! @shahidkapoor," she posted.
Genelia D'Souza, who recently gave birth to her second child, congratulated Mira and the "Shaandaar" star.
"Congratulations @shahidkapoor and Mira... It's the world's best feeling and I'm sure you already know how it is..
Lots of love to the little one," she tweeted.
Meanwhile, Riteish Deshmukh posted, "Congratulations @shahidkapoor and Mira on birth of an angel... Welcome to the club my friend. Love and blessings to the little one."
Director-choreographer Farah Khan said the parents can take any advice from her related to their newly born child as she is already a qualified mother of three.
"Heartfelt Congratulations 2 Mira n @shahidkapoor .. God bless your little Angel.. And any advice you need I'm thrice qualified," she wrote.
Shahid and Mira got married last year in July.
On the work front, Shahid will next be seen in Vishal Bharadwaj's "Rangoon," which also stars Saif Ali Khan and Kangana Ranaut