"Dangal" editor Ballu Saluja, costume designers Manish Malhotra and Dolly Ahluwalia, cinematographer Anil Mehta, actress Madhabi Mukherjee, production designers Subrata Chakraborthy and Amit Ray are also a part of the list.
Ali, who featured with Judi Dench in "Victoria and Abdul", tweeted: "So so humbled to be included with the greats. Thank you The Academy for this membership. I look forward to this friendship for a long long time..Sending my love from India."
Monga, known for producing "The Lunchbox" and "Masaan", wrote on Instagram: "Honoured to have been invited to become a member of the Academy of Motion Picture Arts and Sciences. Class of 2018 !!!!! Thank you The Academy."
The Academy extended invitations to a record 928 artistes and executives who have distinguished themselves by their contributions to theatrical motion pictures across the world.
Those who accept the invitations will be the only additions to the Academy's membership in 2018, read a statement.
Among the invitees, 17 are Oscar winners, while 92 are Oscar nominees, including Timothee Chalamet and Daniel Kaluuya.
Forty-nine per cent of the class of 2018 are female, and, should all accept membership, that will bring overall percentage of women in the Academy to 31 per cent.
Thirty-eight percent of the new invitees are people of colour, which, should they all accept, would bring their overall percentage of the Academy to 16 per cent, according to hollywoodreporter.com.
Tiffany Haddish, Kal Penn, Kumail Nanjiani, Blake Lively, Dave Chappelle, Mindy Kaling, George Lopez, Amy Schumer, Sarah Silverman, Evan Rachel Wood, Naveen Andrews, Melissa Etheridge, Jada Pinkett Smith, Kendrick Lamar and J.K. Rowling are among the popular names on the list which ranges from actress Quvenzhane Wallis, who, at age 14, is the youngest, to composer Sofia Gubaidulina, who, at 86, is the oldest.