Mrs Johnson revealed the happy news with an Instagram post on Saturday, July 31.
Mrs Johnson, 33, also revealed on Instagram that she suffered a miscarriage earlier this year.
She said the couple’s ‘rainbow baby’ is due around Christmas.
She wrote: “Hoping for our rainbow baby this Christmas.
“At the beginning of the year, I had a miscarriage which left me heartbroken.
“I feel incredibly blessed to be pregnant again but I’ve also felt like a bag of nerves.”
She and Mr Johnson, who were married in May, also have 15-month-old son Wilfred together.
The couple made the announcement only two months after they tied the knot during a low-key wedding at Westminster Cathedral.
Ms Johnson, a former Conservative Party communications director, said she wanted to share the personal news about her miscarriage to “help others”.
She added: “Fertility issues can be really hard for many people, particularly when on platforms like Instagram it can look like everything is only ever going well.
“I found it a real comfort to hear from people who had also experienced loss so I hope that in some very small way sharing this might help others too.”
Downing Street said the Prime Minister had been due to work this weekend from his official country residence Chequers in Buckinghamshire, although it is not known if the couple are there together.