Video report by ITV News Correspondent Angus Walker
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.
Dominic Raab, who is running against Mr Johnson in the leadership contest, made similar claims during the referendum campaign and sidestepped a question from ITV News about whether he would stand by his rival in court to defend the claims.
He said: "I do worry a little bit about the timing of this. The cut and thrust of democratic debate ought to be decided by your viewers rather than in court."
A date has not yet been set for a court hearing, but could come after the Tory leadership contest has concluded - meaning Mr Johnson, if he wins the race, may face trial as prime minister.
His first appearance at magistrates' court could occur during the contest.
But Jacob Rees-Mogg, who is backing Mr Johnson for Tory leader, told ITV News the prosecution was "politically motivated" and that the statement was "clearly justifiable".
ITV News spent a day on the 2016 referendum campaign trail with Mr Johnson when he was pressed repeatedly on the £350 million claim.
He defended the figure and insisted it was correct "on gross terms" - although he did concede that the UK did receive a substantial amount in grants.
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.
Mr Johnson did not say anything later on Wednesday when reporters caught up with him.
Earlier, his position was outlined in the ruling, describing 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.
"The reality of this enterprise is different. The 'Prosecutor' (a limited company) is 'Brexit Justice Limited'.
"Brexit Justice Limited is the product of a campaign to undermine the result of the Brexit referendum, and/or to prevent its consequences.
"The company and this application owe their existence to the desire on the part of individuals such as Mr Ball to undermine the referendum result. The 'Brexit justice' which is ultimately sought is no Brexit."
Gina Miller, who was instrumental in leading a legal challenge against the Government in pushing Brexit through without Parliamentary approval, told ITV News it was important for the courts to be able to scrutinise politicians' claims.
However, she said, no one could have foreseen a leadership race being launched just as Mr Ball's case came to court - it was, she said, an accident of timing.
That said, the case raised an important issue that MPs should be held to account.
Further outlining her reasoning to allow the case to proceed, Judge Coleman added that Mr Ball believes there is "ample evidence" Mr Johnson knew what he was saying was false.
"One example is given that in a televised interview in May 2016 the proposed defendant stated, 'we send the EU £10 billion per year' and that therefore he knew that the £350 million per week figure (£20 billion per year) was incorrect," she wrote.
She said: "I accept that the public offices held by Mr Johnson provide status but with that status comes influence and authority.
"I am satisfied there is sufficient to establish prima facie evidence of an issue to be determined at trial of this aspect.
"I consider the arguments put forward on behalf of the proposed defendant to be trial issues."
Conservative former cabinet minister and barrister David Mellor said the ruling was a "deplorable absurdity", and that courts should not adjudicate on what politicians do during election campaigns.
"I imagine there will be no shortage of senior judges who will feel acutely embarrassed about this," he said.
"Politicians at election times exaggerate, and say things that may or may not be true, and it's the electorate, not the courts, who should decide whether they are reliable or not."
And one of Johnson's rivals for the leadership, Health Secretary Matt Hancock waded in to also denounce the ruling.
"However people voted in the referendum, we shouldn't have courts judging on political debates," he said.
"Let's have robust debate to test arguments - and keep courts out of politics."