Under current Covid rules there is a limit of 30 guests at weddings - although the cap is expected to be lifted on June 21 - "freedom day" - when most restrictions are set to be lifted.
When elected in 2019, Boris Johnson became the first prime minister to live at Downing Street as part of an unmarried couple.
Downing Street has declined to comment.
The Sun said senior Downing Street aides did not know about the wedding.
This morning Downing Street confirmed the couple tied the knot yesterday afternoon in a "small ceremony" at Westminster Cathedral after an extraordinary cloak-and-dagger operation to keep the event secret - with a bigger celebration planned for next summer.
The weekend nuptials were a surprise development, after reports earlier this week said the couple had sent out "save the date" cards for a wedding on 30 July next year.
The Sun reported that an unnamed member of staff said that when Symonds walked down the aisle, Johnson "didn't take his eyes off her".
Their son, Wilfred, was born last April.
This is Johnson's third marriage.
He was previously married at the age of 23 to Allegra Mostyn-Owen in 1987.
The wedding comes at the end of a hard week for the prime minister in which his former aide Dominic Cummings branded him unfit for office.
However, they have been waiting months to tie the knot after their original plans to marry a year ago were delayed by the pandemic.
Johnson, who has faced several bruising days of scrutiny after his former top aide Dominic Cummings lambasted his government's handling of the coronavirus pandemic in front of a parliamentary committee Wednesday, has been married twice before.
Although there was no official confirmation of the wedding, congratulatory messages were posted on social media, the BBC reported.
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.
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.