Sharing the news on Instagram, Mrs Johnson said she had felt "pretty exhausted" for the past eight months but "we can't wait to meet this little one" in a few weeks' time.
The couple, who married in May 2021, already have two children - three-year-old Wilf and two-year-old Romy.
Mr Johnson has four children from his previous marriage to Marina Wheeler.
Writing on Instagram, Mrs Johnson said: "Wilf is v excited about being a big brother again and has been chattering about it nonstop.
"Don't think Romy has a clue what's coming…She soon will!"