The player - known mononymously as Bala - has signed an 18-month deal with the Light Blues after a successful trial spell in November last year.
She is India's leading scorer, having netted 52 goals in 58 matches since 2010. She has also scored more than 100 times in 120 appearances at club level.
Bala is Rangers' first Asian international footballer, and the two-time winner of the All India Football Federation (AIFF) Women's Player of the Year award is hopeful that her groundbreaking transfer can help inspire her compatriots.
Speaking to the Ibrox club's official website, she said: "To play my football in Europe with one of the biggest clubs in the world is something I could never have dreamed of.
"I hope my move to Rangers serves as an example to all the women footballers back home in India who dream of taking up the sport professionally.
"I'm looking forward to making the most of the top-class facilities and coaching and I am certain I will benefit immensely from the standard of training and competition."
Team manager Amy McDonald welcomed the "exciting signing", saying: "Bala is a playmaker who likes to play as a number 10 and we believe she will contribute goals and assists to the team.
"She is already a role model for girls across India and they will now be able to see her travel across the world to become a professional footballer."
Rangers head of academy Craig Mulholland added: "I would like to warmly welcome Bala to both Rangers and to Glasgow.
"We believe this is a huge step for the women's game both in Scotland and in general. We are committed to building a successful women's team for years to come and the acquisition of a talent like Bala is another step towards our goal of domestic and European success."
A serving police officer with Manipur Police Department, Bala has won three SAFF Women's Championship titles and two gold medals at the South Asian Games, and has had spells with Eastern Sporting Union and Kangchup Road Young Physical and Sports Association (KRYPHSA) FC as well as Manipur Police Sports Club.