"We are blessed to have two healthy girls – we are so grateful," Piazza, 41, tells PEOPLE.
Paulina arrived on Aug. 3 at Mount Sinai Medical Center in Miami, weighing 6 lbs., 3 oz., and measuring 24½ inches long. She and mom Alicia, 37, an actress and former Playboy model, are healthy and happy, says a Piazza rep.
Paulina is the Piazza's second daughter. Big sister Nicoletta Veronica, 2 ½, is thrilled with her new little sister, and Piazza says that having two kids is double the fun. "Being a father – it's the most rewarding thing I've ever done," he says.
When the former catcher – who announced his retirement on May 20, 2008 – is not changing diapers and burping babies, he's busy coaching the Italian national team entry for the World Baseball Classic. As he said prior to Paulina's arrival, "I'm excited to be at home and enjoy moments with my kid."