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 Markaz