Here are some key elements of the proposals laid out in an article for the Daily Telegraph.
A “failure of government”
Mr Johnson said a “pretty invertebrate performance” in the Brexit negotiations had seen a “collective failure of government” that had ended with the Chequers plan.
He is calling for Theresa May to “chuck” her Brexit proposals, renegotiate the arrangements for Britain’s withdrawal from the EU and go to Brussels with his plan for the future relationship.
What does Mr Johnson say is wrong with Chequers?
The plan agreed by Cabinet - including Mr Johnson before his resignation as foreign secretary - will result in “enforced vassalage” of Britain to the EU, he said.
UK firms will be exposed to EU regulations, which could be designed to disadvantage them. Free trade deals will be made “doubly difficult” due to Britain not having control over regulations for good and agri-foods, he said.
The EU will also be able to enforce tariffs at Britain’s borders, while Parliament would have to give up control of an “entire corpus” of laws to the European Court of Justice (ECJ).
What is he suggesting?
Mr Johnson has proposed a model for a free trade deal he calls “SuperCanada”, with all the benefits of the EU-Canada Comprehensive Economic and Trade Agreement (CETA).
Under a new withdrawal agreement the UK and EU will have until 2020 to sign off the deal.
What is Canada’s arrangement with the EU?
CETA is the most extensive signed by the EU with an external country to date.
It allows Canada to access the European market on improved terms while not being a member, so it does not have to pay into the EU budget, follow ECJ laws or adopt freedom of movement.
Under CETA, nearly all tariffs are being eliminated on imports and exports between the countries, while there are increased opportunities for companies to do business and workers to move between the territories.
This is supported by closer cooperation on regulation and intellectual property. It has not done away with border controls.
What is the “super” bit?
Mr Johnson says cooperation between the UK and EU would be closer on areas such as defence, security and aviation. There would also be “extensive provisions on services”, which make up the majority of the UK economy. This would be based on, but go further than, the CETA model.
Why is this not already the plan?
Critics including the Prime Minister say a CETA-style deal would still result in customs checks between the Republic of Ireland and Northern Ireland, which could jeopardise the Good Friday Agreement. The EU has said that without proper checks an open border would harm the integrity of the single market.
How does SuperCanada get around that?
Mr Johnson says UK and EU regulatory bodies would ensure conformity of standards “in the spirit of trust and common sense” because “we all want high standards”.
These would use Mutual Recognition Agreements to marry up UK and EU regulations. It will get around the issue of the hard border in Ireland by using technology.