Aishwarya Rai was featured on the cover of Time magazine in 2003 as Bollywood's leading lady and had been interviewed by Oprah Winfrey and David Letterman.
She is one of the top Bollywood actresses and has had several hit movies over the past few years and the announcement of their engagement ends frenzied speculation in the Indian media about the couple.
Abhishek Bachchan has starred in several successful films and was voted the sexiest Asian man by a British newspaper last year and he is the the son of Bollywood superstar Amitabh Bachchan.
In the past, Ms Rai has been linked to other Bollywood actors including Salman Khan and Vivek Oberoi.
Abhishek Bachchan was engaged to former actress Karisma Kapoor but the marriage was subsequently canceled.
