Her Majesty had been at a private hospital in central London for preliminary checks after “reluctantly” cancelling a trip to Northern Ireland on medical advice.
She returned to Windsor Castle at lunchtime on Thursday in “good spirits” and carried out light duties in the afternoon.
Speaking to reporters on a visit to a vaccine centre at the Little Venice sports centre in west London, Mr Johnson said: “I think everybody sends Her Majesty our very, very best wishes.
“And certainly we have from the government.
“But I’m given to understand that actually Her Majesty is characteristically back at her desk at Windsor as we speak.
“But we send her every possible good wish.”
A Downing Street spokesperson declined to say whether Mr Johnson had held his weekly audience with the 95-year-old monarch.
Buckingham Palace said the Queen underwent tests at King Edward VII’s Hospital following the cancellation of her trip to Northern Ireland, which had been planned to mark the centenary of its creation.
The medical issue was not related to Covid, officials said.
The palace does not normally offer a running account of the monarch’s health, citing her privacy. However, in this case it confirmed the queen’s hospital stay after the Sun newspaper reported the news.
On the whole, there is a rule of thumb that if a senior member of the royal family undergoes a procedure or an operation, there is a medical bulletin, royal expert Robert Hardman told the BBC. But that doesn’t apply to tests, he said.
The attention paid to the development merely reflects the great affection the global community has for the monarch, said Mr Hardman, author of Queen of the World, a book that chronicles the monarch’s influence and stature around the globe.
“She hates people making a fuss of her in general, but particularly to do with health,” he told the BBC.
“And I think there’s a concern to maintain the dignity of the office, and I know that one reason why nothing was said about yesterday’s trip to hospital was that they didn’t suddenly want huge banks of cameras and 24-hour news setting up outside the hospital.”
There has been some disquiet this week about the Queen’s health. A few days ago she was seen using a walking stick at a Westminster Abbey service marking the centenary of the Royal British Legion, an armed forces charity.
Though she has previously used a cane in 2003, it was after she underwent knee surgery.
Focus then turned to her hectic schedule, which has in recent days included audiences with diplomats, a reception at Windsor Castle for global business leaders, and attending a horse race at Ascot Racecourse.
Her Majesty is due to host world leaders at the Cop26 climate summit in Glasgow in just over a week’s time.
Queen Elizabeth is Britain’s longest-lived and longest-reigning monarch. She is due to celebrate her platinum jubilee – 70 years on the throne – next year.
She has ruled since 1952 and was widowed earlier this year when Prince Philip died at the age of 99 in April. She has cut back on her workload in recent years, but still keeps a busy schedule of royal duties.
Register for free to continue reading
Registration is a free and easy way to support our truly independent journalism
By registering, you will also enjoy limited access to Premium articles, exclusive newsletters, commenting, and virtual events with our leading journalists
Already have an account? sign in
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies