Jennifer Lopez and Marc Anthony's newborn twins are named Max and Emme, Lopez's manager Simon Fields officially confirms to PEOPLE.

The new parents welcomed their son and daughter on Feb. 22. Emme was born at 12:12 a.m. and weighed 5 lbs. 7 oz., and Max followed at 12:23 a.m., weighing 6 lbs.

Already gifts have been pouring in for the twins, including pillows and baby carriers from Baby K'tan in Fort Lauderdale with their names embroidered on them, a source tells PEOPLE.

The twins are the first children for Lopez, 38, and the fourth and fifth for Anthony, 39.