The paper said details of where they will marry remained a secret.
Downing Street and aides to the Prime Minister declined to comment on the report.
The couple announced their engagement – together with the news that they were expecting their first child – in February last year.
The paper suggested they had delayed the wedding until 2022 to ensure it was not disrupted by Covid restrictions.
Currently, a maximum of 30 people are allowed to attend a ceremony or reception in England.
In Wales, wedding receptions can have up to 30 people indoors and 50 people outdoors, a limit of 50 applies in Scotland to weddings and receptions and there is no limit on the numbers in Northern Ireland for ceremonies – venues must decide how many people they can safely welcome – but receptions are not currently permitted.
It will be Mr Johnson’s third marriage, having finalised his divorce from his second wife Marina Wheeler in 2020.
He and Ms Symonds have a son, named Wilfred Lawrie Nicholas Johnson in a tribute to their grandfathers and the doctors who helped save Mr Johnson’s life when he was in hospital with Covid-19.
Born in April 2020, Wilfred was the third baby born to a serving prime minister in recent history.