Ian Murray and Martin Whitfield said they would support remaining in the European Economic Area (EEA) in a Commons vote expected in the next two weeks, and called on the Labour leadership to reverse their opposition to staying in the single market.
MPs will get a vote on whether the UK should stay in the EU single market as a member of the EEA, after peers in the House of Lords defeated the government to attach an amendment to the EU Withdrawal Bill.
Almost half of Labour peers rebelled against a party whip to abstain on the amendment, prompting calls from Labour MPs for the leadership to reconsider.
A spokesman for Mr Corbyn said on Wednesday that Labour wants a “new relationship with the single market” and hinted that it will not abandon its position to defeat the government.
"We’re trying to make the case for a Brexit that puts the economy and jobs and living standards first and to unite as much of the country on both sides of the Leave/Remain divide together in negotiating a jobs-first Brexit,” the spokesman said.
"The EEA membership includes a number of different types of relationship, but it’s not what we are proposing.”
In a joint statement, Mr Murray - who resigned as shadow Scottish Secretary in protest at Mr Corbyn’s leadership - and Mr Whitfield said the vote for the EEA in the Lords “shows that the fight against a hard Brexit is far from over”.
“Labour peers have forced the Prime Minister to give MPs a vote on remaining in the European Economic Area, and when that time comes we will vote in favour of doing so,” the MPs said.
“We know we will be joined by many of our party colleagues from England and Wales, other opposition parties and a number of Tory MPs. If the Labour leadership wants to, we can now stop a hard Brexit in its tracks.
“There is no such thing as a good Brexit, but if we are to leave the EU then the least-worst option – to protect jobs and defend rights – is permanent UK membership of the Single Market.
“We urge our colleagues in Scottish Labour and the Labour leadership at Westminster to stand up for workers and defeat Theresa May’s destructive Brexit.”
Meanwhile, Boris Johnson told MPs he is "completely in conformity" with the government's Brexit policy after dismissing the Prime Minister’s preferred option for customs as “crazy”.
The Foreign Secretary said he had not breached the ministerial requirement for collective responsibility, because the customs approach has yet to be decided.
During a statement on the Iran nuclear deal, Tory ex-cabinet minister Ken Clarke congratulated the Foreign Secretary for his "unswerving loyalty to collective Government policy".
Mr Johnson shot back that he remembered writing stories about Mr Clarke's own "unswerving loyalty" over Europe while a journalist before defending his remarks.
The Foreign Secretary added: "I'm completely in conformity with Government policy on the matter I believe which he is referring since that policy has yet to be decided."