Kobe Bryant's Daughter Natalia Accepted Into USC, Vanessa Says 'Daddy Is So Proud'

The Black Mamba's daughter is now a cardinal and gold Trojan ... Natalia Bryant just got accepted into USC on Tuesday -- and Vanessa says Kobe would've been "so proud!"

Vanessa shared the amazing news with heartwarming videos ... showing a PUMPED Natalia after she got her acceptance letter into the University of Southern California.

In one of Vanessa's vids of the special moment, 18-year-old Natalia jumped up and down over and over again ... and screamed "I got in!" repeatedly.

In the other Vanessa video, she showed off all the gifts she gave Natalia for the accomplishment ... and they included balloons, USC swag and some custom Trojan-themed Kobe kicks.

"Tears of joy," Vanessa said of the moment. "I’m SO happy for you Nani! I know daddy is so PROUD OF YOU. I am so PROUD OF YOU!! Your hard work and dedication was so worth it."

"You pushed through the most excruciating pain imaginable and you succeeded. I wish Daddy and Gigi were physically here to celebrate but I know they’re here in spirit. We love you so much!"

Natalia made it pretty clear she's USC-bound after the acceptance letter ... posting a pic of her in SC gear and writing, "See You Soon."

It's been a really good past few weeks for Natalia ... remember, she just signed a deal in February with IMG Models that she was also stoked about.

Kobe was a big USC guy -- who not only attended basketball and football games but also spoke to classes, according to reporter Arash Markazi.