The four brothers were delivered by a Caesarean section at 31 weeks.
The odds of conceiving two sets of identical twins naturally are one in 70 million.
The parents, Tressa and Manuel Montalvo Jr, already have a 2-year-old son, Memphis, and were hoping to give him a brother or a sister. They didn't use any fertility drugs.
Tressa said to Reuters: "We planned the pregnancy - I guess we just succeeded a little too much!"
She was told at her 10-week scan that she would be having twins. The doctor discovered another heartbeat at her next scan, and it showed that she would be having four babies.
As each set of twins shared one placenta, they can't be classed as quadruplets.
Ace and Blaine were born on February 14 at 8.51am, followed by Cash and Dylan a minute later. All the babies weighed under 4 pounds (1.8kg).
"We tried to stick to the A-B-C-D theme when naming them," Tressa said.
"We didn't expect it, we were trying for just one and we were blessed with four."
The couple also revealed that they still want a daughter.