The Mail on Sunday newspaper reported that about 30 people attended the wedding on Saturday, which is the maximum now allowed under measures to limit the spread of the coronavirus.
The photograph issued by Number 10 shows the couple gazing at each in Downing Street's garden after the wedding.
The Sun and Mail on Sunday newspapers said guests were invited at the last minute to the central London ceremony, and said even senior members of Johnson's office were unaware of the wedding plans.
"The couple will celebrate their wedding with family and friends next summer", a spokesperson of Downing Street was quoted in the report.
According to the Daily Mail report, the development came six days after Johnson and Symonds "sent out save-the-date cards to guests telling them to keep Saturday, July 30, 2022 free for a marriage celebration".
The couple has a one-year-old boy named Wilfred.
This is Johnson's third marriage.
He was previously married to Allegra Mostyn-Owen.
He Wednesday Allegra Mostyn-Owen in 1987, but that marriage was annulled in 1993 - the same year he married Marina Wheeler.
Johnson and Symonds had been waiting for months to tie the knot, after being forced to delay their plan past year due to the Covid-19 epidemic.
Several politicians have congratulated the couple, including Home Secretary Priti Patel, Vaccines Minister Nadhim Zahawi and Work and Pensions Secretary Therese Coffey.
The couple have been in the spotlight in recent weeks over an investigation into a scandal over the high cost of redecorating their Downing Street apartment.
Johnson's aides were not informed of the ceremony in advance.
Johnson, 56, and 33-year-old Symonds, an environmental advocate, announced their engagement in February 2020 and have a son together, 1-year-old Wilfred. "Whatever our political differences, I wish them a happy life together".
But former Labour frontbencher Jon Trickett said the wedding was "a good way to bury this week's bad news" on Mr Cummings' testimony, the spread of the Indian coronavirus variant and the row about funding of the Downing Street flat.