He suggests that Britain must use its "defence budget" to stop the establishment of a "terrorist caliphate" in the Middle East or a "tide of terror will eventually lap at our own front door".
His intervention came as Britain's ambassador to the US said intelligence agents believe they have identified the "jihadi John", the Briton responsible for beheading US journalist James Foley, after employing sophitsticated voice recognition technology.
Peter Westmacott, the UK's ambassador to Washington, also disclosed that 70 militants have been arrested after returning from Syria, a number of them carrying instructions for "very specific missions" to unleash terrorist atrocities on British soil.
Mr Johnson says that Britain needs to help "close down" the Islamic caliphate before it is too late, adding that "doing nothing is surely worst of all".
He says: "If we let Isil get their way, then we will be acquiescing, first, in a gigantic and violent change in international borders.
"Next, we will be allowing a new and hideous regime to be born, a country where black-flag waving jihadis compete to show they have the most bigoted and reactionary understanding of their religion by persecuting women, Jews, Christians, gays, Yazidis ande Shiites.
"The place would be a giant training ground for terrorists and wannabe jihadis. We need to try to close it down now, before it gets worse."
Senior lawyers said that Mr Johnson's proposals for "rebuttable presumption" would mark a "profound change" to British law.
Earlier this year, David Cameron announced new laws under which terrorist offences committed in Syria will be prosecuted as if they have taken place on British soil.
The lawyers said Johnson's plans will go significantly further by shifting the burden of proof from police and prosecutors onto suspected jihadists.
Mr Johnson also says that suspected terrorists who do not return to Britain and "continue to give allegiance" to Isil should be stripped of their citizenship. Similar calls have been made by David Davis, the Tory MP, and Lord Carey, the former Archbishop of Canterbury.
He challenges the Liberal Democrats to support control orders, which were axed by the Coalition amid concerns that they infringed on human rights.
On Sunday it emerged that Peter Theo Curtis, an American journalist kidnapped nearly two years ago, has been freed in Syria and handed over to UN officials.