Corbyn said that the strikes were "legally questionable" and that he would use the debate to push for a new "War Powers Act" that would ensure all future government leaders required MPs' approval before taking nearly any military action.
The Ilford South MP, Mike Gapes, pointed to intervention directed by earlier Labour governments without United Nations approval in Sierra Leone, Kosovo and elsewhere, saying: "There is a longstanding and noble tradition on these benches supporting humanitarian intervention and the responsibility to protect".
Foreign Secretary Boris Johnson promised MPs would have "abundant time" to have their say.
Speaking in Downing Street after Friday night's military action against Bashar al Assad's regime, the Prime Minister said the strikes had been limited in response to an alleged chemical weapons attack in Douma last weekend.
Both Syria, which denies any chemical use, and Russian Federation, which provides military support to the Syrian government, have reacted angrily to the action.
Corbyn won approval for a debate on parliament's rights in regard to British military action on Tuesday, and parliament debated long into the evening on Monday on the government's strategy in Syria, particularly regarding civilians there.
It returns from its break on Monday, when May will face MPs' questions on the strikes.
BBC political correspondent Ben Wright said if approved it would be up to the opposition parties to decide if they wanted a vote at the end of the debate.
"If and when such a thing were to happen then clearly, with allies, we would study what the options were."May, whose leadership has been questioned after scandals, divisions over Brexit and an ill-judged election that lost her party its majority in parliament, has found support from other global leaders for backing action against Syria". Some people will suspect that that didn't happen because of governmental concerns that they couldn't get the vote in Parliament.
Lawmakers backed action in Iraq in 2014, and again in Syria in 2015, strictly limiting strikes in both countries to targets of the Islamic State jihadist group.
But she will say the United Kingdom joined the USA and France in co-ordinated strikes following the chemical weapons attack in Douma to "alleviate further humanitarian suffering".
Such a position would mean, Grieve argued, "that any tyrant, megalomaniac, person intent on carrying out genocide, if they have the support of an amoral state within the security council, they will be able to conduct that genocide with total impunity, even if it was within our power to act to prevent it".
"Governments have to bear in mind the need to be able to act swiftly and flexibly and to protect the safety of our servicemen and women", he added.
For its part, the Scottish National Party says it will force a vote on the issue.
Mr Corbyn, who has warned of an escalation in a "proxy war" between the USA and Russian Federation, said he would only consider backing intervention in Syria with the support of the United Nations.
"That surely would save a lot of lives".
French Prime Minister Edouard Philippe also justified the military action in a speech Monday to the National Assembly, France's lower house of parliament.
Four Royal Air Force Tornado GR4s joined the co-ordinated missile strikes at 2am, launching Storm Shadow missiles at a base 15 miles west of Homs.
At an emergency meeting of the UN Security Council, US ambassador Nikki Haley warned if there was further use of chemical weapons in Syria, America is "locked and loaded".
North Atlantic Treaty Organisation allies have given the action their full support, Secretary General Jens Stoltenberg said.