"Both mom and baby are healthy and doing great," Rob told People. "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.
"She is a perfect baby and we could not have asked for anything more. We are over the moon with happiness at her arrival!"
The baby's middle name is a tribute to Rob's grandmother, who passed away on the same day she was born.
"[We plan to start a family] not, like, tomorrow soon, but pretty soon," Rob told OK! Weekly in early 2007.
The belated birth announcement -- which also wasn't proceeded by a public pregnancy announcement -- represents a low-profile change for the couple, who previously got engaged and married on television.
Rob and Amber first met when Survivor: All-Stars was filmed in Panama in late 2003. Amber had previously appeared on Survivor: The Australian Outback, which aired in early 2001, while Rob had competed on Survivor: Marquesas, which was broadcast in early 2002.
The next spring, Rob (the other member of Survivor: All-Stars' Final 2) publicly proposed to Amber just before Survivor host Jeff Probst revealed he had finished second and Amber had won the competition's $1,000,000 grand prize during the show's May 2004 live finale.
Later that year, Rob appeared as the "Player Operator," a secret Charlie's Angels-like telephone voice on UPN's The Player reality dating series.
In 2005, the duo returned to the CBS schedule and appeared on The Amazing Race 7, where -- in a familiar situation for Rob -- they finished second. Later that spring, they were married in an April 2005 destination wedding which served as the basis of Rob and Amber Get Married, a reality TV special that aired on CBS in May 2005.
The following year, Rob headlined Sci Fi Investigates, a six-episode Sci Fi Channel reality series which investigated and tried to explain paranormal and supernatural phenomenon.
After also starring in Rob and Amber: Against the Odds, a Fox Reality Channel series which featured the couple relocating to Las Vegas so Rob could attempt to become a professional poker player, Rob and Amber returned to The Amazing Race a second time and competed in the show's All-Stars edition in early 2007.
Despite finishing in first place during the race's first three legs, Rob and Amber were the fourth team eliminated from The Amazing Race: All-Stars.