The favourite to win the Tory leadership race faces a private prosecution by campaigner Marcus Ball.
Lawyers representing Mr Ball lodged an application to summons Mr Johnson to court, claiming he had deliberately misled the public during the Brexit referendum campaign in 2016 and then repeated the statement during the 2017 general election.
In a written decision, District Judge Margot Coleman said Mr Johnson will be summonsed to court.
She wrote: "The allegations which have been made are unproven accusations and I do not make any findings of fact.
"Having considered all the relevant factors I am satisfied that this is a proper case to issue the summons as requested for the three offences as drafted. The charges are indictable only.
"This means the proposed defendant will be required to attend this court for a preliminary hearing, and the case will then be sent to the Crown Court for trial.
"The charges can only be dealt with in the Crown Court."
Mr Ball has raised more than £200,000 through a 'Brexit Justice' crowdfunding campaign to pay for the private prosecution.
A section of the judge's ruling included Mr Johnson's position, which described the application as a "[political] stunt".
His position in summary said: "This application is brought for political purposes. The position presented to the court is that this is a disinterested attempt to improve the standards of political debate."
It added: "The application is a [political] stunt. Its true purpose is not that it should succeed, but that it should be made at all. And made with as much public fanfare as the prosecution can engender."
Lewis Power QC, representing Mr Ball, told Westminster Magistrates' Court last week: "Democracy demands responsible and honest leadership from those in public office.
"The conduct of the proposed defendant Boris Johnson was both irresponsible and dishonest. It was, we say, criminal."
Mr Power said the prosecution's application was not brought to undermine the result of the Brexit referendum and was not about what could have been done with the saved money.
He said: "The allegation with which this prosecution is concerned, put simply, is Mr Johnson repeatedly misrepresented the amount that the UK sends to Europe each week."It is concerned with one infamous statement: 'We send the EU £350m a week'.
"The UK has never sent, given or provided £350m a week to Europe. That statement is simply not ambiguous."
Adrian Darbishire QC, representing Mr Johnson, said his client denies acting dishonestly.
Mr Ball has raised more than £200,000 through a "Brexit Justice" crowdfunding campaign to pay for the private prosecution.
Originally from Norfolk, he has worked full-time on the prosecution case since June 2016.
Mr Ball previously said he and his backers "aspire to set a precedent in the UK common law making it illegal for an elected representative to lie to the public about financial matters".