She announced the arrival of Albert Louie Kenny on Instagram, with a photo of her alongside husband Jason - a six-time Olympic gold medallist.
She said he was born late on Wednesday, a week over his due date.
"Welcome to the world little Albert Louie Kenny. 23/08/17 8lb 12.5oz 22.44. You kept us waiting a week but it was all worth it," she wrote.
The 25-year-old, whose hometown is Cheshunt in Hertfordshire, retained the team pursuit and women's omnium titles in Rio that she won at London 2012.
She has already declared her intention to compete at a third Olympic Games in Tokyo in 2020 but has said she will not rush back to the sport.
Jason has seven Olympic track sprint medals to his name - including six golds - making him the holder of the most titles for a Briton alongside former team-mate Sir Chris Hoy.
The relationship between the pair began during the build-up to the London 2012 Olympic Games and they married in Cheshire in September.
Friend and fellow cyclist Dani King tweeted she "cannot wait to meet him".
While Paralympic cyclist Dame Sarah Storey - who is expecting her second child - said it was "lovely news".
End of Twitter post  by @DaniKing1
Four-time Olympic cycling champion Laura Kenny has given birth to her first child.