Kobe, an 18-time NBA All-Star who won five championships during his 20 seasons with the Los Angeles Lakers, also announced his daughter's arrival on Instagram.
"We are beyond excited that our baby girl 'Koko' has arrived!!" Bryant wrote.
Capri is the youngest Bryant child after 16-year-old Natalia, 13-year-old Gianna and two-year-old Bianka.
The Bryants' children are all girls, which the couple has discussed in past interviews.
Kobe said his wife wanted a son in a 2017 interview with Extra.
"I hear boys are just walking tornadoes," he said. "We'll see. I think Vanessa wants a boy more than I do."
He also discussed the family on The Ellen DeGeneres Show (h/t Helen Murphy of People) in April.
"I love my princesses," Bryant said. "Vanessa was kind of putting the pressure on me to have a boy: 'You can do it, you can do it!' And then, 'Nah, you can't do it.'"
There's a chance the Bryants may have another child, though.
"I would go for a solid starting five," Bryant said when DeGeneres asked how many kids he would like. "You just have your own internal basketball team."