Johnson told MPs that his proposals which would see Northern Ireland stay in the European single market for goods but leave the customs union were a "compromise". He has maintained that the UK will leave the EU on October 31, with or without a deal.
Opposition Labour Party leader Jeremy Corbyn criticized the "unrealistic and damaging proposals", while the European Commission said there were "problematic points" in the UK's proposal and "further work is needed", the BBC reported.
The UK government is now hoping to begin a period of intense negotiations with the aim of reaching a final agreement at an EU summit on October 17.
"This government has moved, our proposals do represent a compromise and I hope that the House can now come together in the national interest, behind this new deal," Johnson told MPs.
The Prime Minister's proposal aims to replace the Irish border "backstop" in the existing withdrawal agreement which has been rejected three times by MPs.
The backstop is the controversial "insurance policy" that is meant to keep a free-flowing border on the island of Ireland but which critics - including Johnson - fear could trap the UK in EU trading rules indefinitely. It has proved to be the sticking point in negotiations.
"I believe this is our chance and their chance to get a deal," Johnson said. But he added that the two sides were "some way from a resolution".
According to him, the plan would mean there was no need for checks or infrastructure between Ireland and Northern Ireland.
Opposing Johnson's plan, Corbyn said that it would "damage the whole UK economy, the Northern Irish economy especially and would undermine the Good Friday agreement".
Scottish National Party's Westminster leader Ian Blackford said Johnson will "never have the consent of Scotland" for his Brexit deal, saying that he "doesn't grasp the reality of a workable backstop".
A European Commission spokesperson said: "There are, as we have said, problematic points in the UK's proposal and further work is needed, but that work needs to be done by the UK and not the other way around.
"We would remind you that it's the UK leaving the EU and not the EU leaving the UK."
Irish Prime Minister Leo Varadkar said the UK's approach "did not fully meet the agreed objectives of the backstop".
( With inputs from IANS )