Johnson's last marriage was to Marina Wheeler, a lawyer.
He Wednesday Allegra Mostyn-Owen in 1987, but that marriage was annulled in 1993 - the same year he married Marina Wheeler. Even though their divorce finalised in May 2020, they had announced their separation in 2018.
Current coronavirus restrictions in England limit attendants of a wedding ceremony to 30.
But dancing is advised against due to the increased risk of transmission, except the couple's traditional first dance.
Northern Ireland's First Minister Arlene Foster also wished them a "huge congratulations" on Twitter.
The Sun said senior Downing Street aides did not know about the wedding.
The reported nuptials come after a tumultuous political week for Johnson, who was accused by former top aide Dominic Cummings on Wednesday of bungling the government's response to the coronavirus and being "unfit for the job".
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