Mr Johnson, who stepped down as foreign secretary last week, called for the PM to tear up her "miserable" plans for close relations with the EU and return to the "glorious vision" of global Britain which she previously set out.
In a highly-charged personal statement to the House of Commons, Mr Johnson did not directly challenge to Mrs May's position as Prime Minister and Conservative leader.
However, he denounced the plan agreed at Chequers and set out in the PM's white paper last week as a "Brexit in name only" which would leave the UK in a state of "vassalage".
He also made clear his intention to put himself at the forefront of backbench demands to return to Mrs May's original red lines of total withdrawal from the customs union and single market.
Accusing the Government of "dithering" over its Brexit negotiations, he said that a "fog of self-doubt" had descended on Mrs May's stance to EU withdrawal since she first set it out in a speech at Lancaster House last year.
In a 12-minute statement, he said: "It is not too late to save Brexit. We have time in these negotiations.
"We have changed tack once and we can change again.
"The problem is not that we have failed to make the case for a free trade agreement of the kind spelt out at Lancaster House.
"We haven't even tried. We must try now because we will not get another chance to do it right."
Mr Johnson said at Lancaster House Mrs May made clear that she would seek a "bold, ambitious and comprehensive" free trade agreement with the EU outside the customs union and single market.
"I thought it was the right vision then, I think so today," he said.
But he said that since then, "a fog of self-doubt has descended".
He said: "We never actually turned that vision into a negotiating position in Brussels and we never made it into a negotiating offer.
"Instead we dithered and we burned through our negotiating capital."
Mr Johnson said Britain should be "great independent actors" on the world stage, not "rule takers".
"That was the vision of Brexit that we fought for," he said. "That was the vision that the Prime Minister rightly described last year.
"That is the prize that is still attainable. There is time. And, if the Prime Minister can fix that vision once again before us, then I believe she can deliver a great Brexit for Britain with a positive, self-confident approach that will unite this party, unite this House and unite this country as well."