The 73-year-old news anchor said the couple had a baby boy via a surrogate on 2 March after “numerous medical setbacks and miscarriages”.
In a statement to the PA news agency, the broadcaster said: “In our desire to seal our now 11 years of marriage with a baby, my wife suffered numerous medical setbacks and miscarriages.
“Consequently, we will always be deeply grateful to our surrogate, who carried our embryo to term.
“Amid these challenging times, we feel doubly blessed to be able to celebrate our good fortune.”
Jon and academic Precious tied the knot in 2010.
He has two daughters from his relationship with human rights lawyer Madeleine Colvin.
The broadcaster is best known for being the longest-running presenter on Channel 4 News, which he has fronted since 1989.
Precious is an epidemiologist with the Medical Research Council, specialising in HIV prevention in Africa, and a Yale World Fellow.
She also captained the Cambridge University women’s karate team while doing a PhD in neuroscience there a decade ago.