Johnson opened the debate saying his deal with the EU can "heal the country", the BBC reported.
The Democratic Unionist Party and other opposition parties have planned to vote against the Brexit deal.
The MPs will also vote on the so-called Letwin amendment to delay Brexit until necessary UK legislation is passed.
They would also vote on an amendment calling for a confirmatory referendum.
If the Letwin amendment is passed, it would be "too late" for the government to pull the main vote on the deal.
According to reports, Downing Street has suggested that the Letwin amendment increases the chances of a no-deal Brexit.
The Letwin amendment would provisionally approve Johnson's Brexit deal, but withhold official support and delay Brexit until the necessary legislation is passed.
Labour MP Rebecca Long-Baile told the parliamentar that Johnson's deal will add costs and bureaucracy for UK businesses. It will also damage workers' rights, she said.
Meanwhile, tens of thousands of people were marching through central London on Saturday to demand a "final say" vote on Prime Minister Johnson's new Brexit deal.
Organisers of the "People's Vote" campaign said they wanted to ascertain whether new Brexit terms by Johnson were good for the UK.
Protesters were headed to Westminster as MPs debate the new deal in the Commons.
The march, which began at midday on Park Lane, will end in Parliament Square.
( With inputs from IANS )