Pompeo, who is notoriously private, was spotted hiking with the newborn and her family in California this week, before a spokesperson later confirmed that the child was indeed theirs, according to US Weekly.
The 47-year-old mother has since taken matters into her own hands and shared a personal photograph with her 2.8 million Instagram followers, saying: “Chris Ivery has dropped a notch, I’ve got a new guy.”
She also revealed her son’s name, Eli Christopher.
Although it has still not been confirmed exactly how old he is.
Eli is the first boy for the couple, who were married in 2007 by then-New-York-mayor Michael Bloomberg, as they already have two daughters.
Seven-year-old daughter Stella, and two-year-old Sienna, who was welcomed via a surrogate in 2014, and kept secret for several weeks to protect the identity of the surrogate mother.