Rob & Amber Welcome Baby Girl

Reality TV’s most famous couple are taking on a new challenge — parenthood!

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Rob and Amber Mariano, the thrill-seeking stars of Survivor, The Amazing Race, and Rob and Amber: Against the Odds, welcomed their first child on July 4, new dad Rob, 33, revealed to PEOPLE on Monday.

The couple honored Rob’s great-grandmother, Rose, who died July 4, by naming their baby girl after her. Amber, 30, gave birth to daughter Lucia Rose, who weighed in at 6 lbs., 11.5 oz. and measured just over 19 in. at Sacred Heart Hospital in Pensacola.

“Lucia is a great eater and sleeps a lot, however she tends to be a bit of a night owl like her daddy at times,” Rob told the celebrity weekly. “She is a perfect baby and we could not have asked for anything more. We are over the moon with happiness at her arrival!”

Rob and Amber met when they both appeared on Survivor: All-Stars in 2004. Rob proposed during the show’s finale and the pair wed on April 16, 2005.