The cubs are the first litter born to South African lion mother, Adia, 3, and father, Hubert, 13. They're also the first litter born at the zoo since 1991.
The now three-week-old cubs are not ready for public viewing yet, as the zoo is trying to allow plenty of family bonding time in a quieter environment.
"We've been monitoring them the last few weeks by video camera," Martin Ramirez, the zoo's mammal curator, told ABCNews.com. "By using the video, we've been able to tell the mother is taking great care of them. There was one cub early on that was making us very nervous, though.
"She's a first-time mom, and a typical litter size for a first-time mom is two. We were all really excited when she had the one, and then she had two, and then three came along, and we were like 'O.K., wow,' and then the fourth one came along and we were a little worried because that's a handful. That's when we made the decision that we're just going to watch and if we have to intervene, we will."
But not to worry, the fuzzy felines had their first medical exam and wellness check today and are doing very well.
They're doing great," Ramirez said. "We could always see round bellies on them, which is an indication that they're getting enough to eat. At this point they're just drinking mom's milk. But we could see the round bellies on the video. We were seeing normal development on video. Eyes opened when we expected them to open, because they're born with their eyes closed."
The cubs are holding their weight now and are walking normally on their four legs. During the exam, it was also finally determined there are two boys and two girls in the litter.
"Now that we know we have two boys and two girls, we can start looking around for appropriate names. We'll select about 10 or 15 potential names and let the public choose from those," Ramirez said.