Reliance runs multiple TV channels and JioCinema streaming app through its media unit Viacom18 and has a sizeable hold over India's $28-billion media and entertainment market
"He gave me his heart on Valentine's Day, and I said YES!" Lady Gaga, 28, said on Instagram, displaying a photo of a heart-shaped ring.
She and Kinney, 33, have been dating for about four years, according to People magazine.
Lady Gaga, whose hits include "Poker Face" and "Bad Romance," recently won a Grammy Award for her album "Cheek to Cheek" with veteran singer Tony Bennett.
Kinney stars in the NBC series "Chicago Fire."