The fixed penalty notices are the result of a Metropolitan Police investigation into parties in Downing Street and Whitehall in 2020 and 2021.
Mr Johnson will become the first sitting prime minister to receive a punishment for breaking the law.
Labour immediately called for both the PM and chancellor to resign, while Liberal Democrat leader Sir Ed Davey called for parliament to be recalled for a vote of confidence in Mr Johnson.
Scotland's first minister Nicola Sturgeon also demanded they quit and her Welsh counterpart Mark Drakeford said the prime minister must go.
Labour and the SNP also called for parliament to be recalled from recess.
Earlier, the Met disclosed that it had now referred more than 50 cases for fixed penalties as a result of the investigation, called Operation Hillman.
It is understood that across the country there have been few examples of more lockdown fines being issued relating to any single address.
A Downing Street spokesman said: "The prime minister and chancellor have today received notification that the Metropolitan Police intend to issue them with fixed penalty notices."
A spokesperson for the prime minister's wife said: "In the interests of transparency, Mrs Johnson can confirm she has been notified that she will receive a fixed penalty notice. She has not yet received any further details about the nature of the FPN."
No 10 confirmed the prime minister was fined for attending his birthday party in the Cabinet Room in Downing Street in June 2020.
Mrs Johnson's spokesperson said she had paid a fixed penalty notice relating to the gathering and "apologises unreservedly".
Sky News understands Mr Sunak only ever answered a police questionnaire in relation to that one event.
Northern Ireland minister Conor Burns previously claimed Mr Johnson was "ambushed by a cake" at the event, where up to 30 people are said to have gathered and sung Happy Birthday.
A YouGov poll has revealed 57% of people think Mr Johnson should resign as prime minister after being fined for attending the party, while 30% said he should stay.
The same proportion of the 2,464 adults polled said Mr Sunak should also resign as chancellor for being at the same event. Some 75% of responders said they thought Mr Johnson knowingly lied to parliament about whether he broke lockdown rules, with just 12% saying he did not.
Labour leader Sir Keir Starmer said: "This is the first time in the history of our country that a prime minister has been found to be in breach of the law, and then he lied repeatedly to the public about it. Britain deserves better, they have to go."
Ms Sturgeon said: "Boris Johnson must resign. He broke the law and repeatedly lied to parliament about it.
"The basic values of integrity and decency - essential to the proper working of any parliamentary democracy - demand that he go. And he should take his out of touch chancellor with him."
Sir Ed said: "The country cannot have criminals and liars leading our government, especially at a time of national and international crisis.
"Boris Johnson and Rishi Sunak took the country's sacrifices for granted, while they broke the law to party in Downing Street.
"They are not fit to hold office. If they had a shred of decency, they would resign."
