"Today was Callum's due date, but he arrived 11weeks early," wrote Sir Chris on 27 December. "Amazing how far he's come since then, we're so thankful."
Sarra Hoy, Chris's wife of four years, retweeted the Edinburgh-born sportsman's message, adding: "Our miracle".
Today was Callum's due date, but he arrived 11weeks early. Amazing how far he's come since then, we're so thankful. pic.twitter.com/1sbfrpot2j— Chris Hoy (@chrishoy) December 27, 2014
Chris and Sarra became parents to their first-born on 15 October.
"Amazed, delighted & a little shocked to announce the birth of our beautiful baby son, Callum David Robert Hoy! Born at 29weeks, today at 2pm", he tweeted to announce the news.
He later added: "Although v.early days for wee Callum, he's doing well as is @SarraHoy. Huge thanks to the incredible medical staff."
Chris and Sarra married in April 2010
Sir Chris became a national treasure after helping to lead Team GB to a record victory at the 2012 London Summer Olympics.
With six gold Olympic medals, he has won more Olympic gold medals than any other British athlete.