In an Instagram post, Mrs Johnson said the baby would arrive “in just a few weeks”.
“I've felt pretty exhausted for much of the last eight months but we can't wait to meet this little one,” she wrote.
“Wilf is [very] excited about being a big brother again, and has been chattering about it non-stop. Don't think Romy has a clue what's coming... She soon will.”
The couple’s first child, Wilf, was born on April 29, 2020.
Their second child Romy, named after Mrs Johnson’s aunt Rosemary, was born on December 9, 2021 at University College London Hospital.
The child will be Mr Johnson’s eighth offspring as he has four children with ex-wife Marina Wheeler, as well as a child born in 2009 with art consultant Helen Macintyre.
It is the first child that the couple have had while not living in Downing Street, which they left in September last year.
The pair’s most recent public appearance was at the King’s Coronation in Westminster Abbey, alongside a host of former Prime Ministers and senior politicians.
Mr Johnson resigned as Prime Minister in July last year following the resignation of a string of Cabinet ministers, including current PM Rishi Sunak.
Since leaving 10 Downing Street, Mr and Mrs Johnson have reportedly been living between a London townhouse and a Cotswolds cottage.
On Monday, The Times reported that Mr Johnson had purchased a £3.8 million, nine-bedroom mansion with a three-sided moat in Oxfordshire.
Meanwhile, the former Prime Minister could face a by-election in his west London constituency if one is triggered following the Commons Privileges Committee probe into partygate.
If found in contempt of Parliament, MPs on the Committee could call for a suspension with a ban of 10 days or more opening the way for a so-called recall petition which could lead to a by-election in Mr Johnson’s Uxbridge and Ruislip seat.
Opposition parties had called for Mr Johnson to pay his own legal fees.
Mr Johnson was paid the advance by the prestigious Harry Walker agency which also boasts Bill Clinton, Barack Obama, Arnold Schwarzenegger and Serena Williams among their exclusive clients.
Since leaving office, the former PM has given a number of lucrative speeches at conferences in Singapore and the US.