Joshi was born in Mumbai[1] to a Gujarati Indian father and an Armenian mother who was born in Lebanon and moved to India. She was brought up in Mumbai where she attended the Jamnabai Narsee School, and later Mithibai College from where she graduated majoring food science and chemistry. She excelled in sports, competing in athletics at the National level. She has two sisters, Selphi and Monalisa. Her sister Monalisa is married to Bollywood actor Rajat Bedi. She has a nephew, Vivann, and niece, Vera.
Tulip entered the Femina Miss India in 2000. She did not make it to the list of winners, but was noticed by many advertising agencies. She appeared in a number of advertising campaigns for big brands (Ponds, Pepsi, Siyaram, BPL, Smirnoff etc.). She also appeared in a video made as a tribute to Nusrat Fateh Ali Khan.
