The pound, which rose sharply on the news, had fallen as low as $1.2997 in the past week.
Talks between May and Corbyn could start as early as today, Brexit minister Robin Walker told Sky News.
Walker said that working with Labour is "not comfortable for us in politics but it is in the national interest".
He also hinted that May could move from her negotiating red lines, "there has to be compromise, that compromise has to come from both sides," he said.
Corbyn said: “I've agreed to meet Theresa May to ensure a disastrous no-deal outcome is prevented, and so Labour can give security and certainty to the people of this country.”
May has been criticised by the pro-Brexit wing of her party for the move with former foreign secretary Boris Johnson calling the decision “very disappointing”.
Johnson said: “It is very disappointing that the cabinet has decided to entrust the final handling of Brexit to Jeremy Corbyn and the Labour Party. It now seems all too likely that British trade policy and key law making powers will be handed over to Brussels – with no say for the UK.”
Joshua Mahony, an analyst at online trading group IG, said: "The GBP gains highlight the feeling that the involvement of Labour will not only raise the likeliness of an eventual agreement, but also drive the direction towards a softer Brexit that could include a customs union."
Speaking after a marathon seven-hour Cabinet meeting last night, the May said if she was Read More