Both Scottish and UK government ministers urged a resolution of the dispute which now requires the company to accept the union's changed position and allow the re-opening of the plant.
Scottish Finance Secretary John Swinney, and Alistair Carmichael, Scottish Secretary, met with owners Ineos and Unite union officials yesterday before talking to workers and council officials in the town.
First Minister Alex Salmond also met with Unite General Secretary Len McCluskey and the union's Scottish secretary Pat Rafferty in Edinburgh.
The union earlier agreed to accept the terms of the company's 'survival plan' involving the ending of the final salary pension scheme and a pay freeze, after Ineos announced it was closing the site down, following the initial rejection of the terms.
Ineos said there would be a statement on the future of the Grangemouth plant today, following yesterday's talks.
Union leaders said the turnaround was not humiliating and the priority was keeping workers in jobs.
Len McCluskey, General Secretary of the Unite union, criticised the management tactics but wanted to ensure Grangemouth had a future.
He said: "We are not going to let this plant close. We are encouraged by the comments of the First Minister that he too will not let this plant close.
"We have a situation whereby a company has put down an ultimatum and we have to respond.
"It is not how we engage in modern-day industrial relations.
"My union is engaged with thousands of companies every day to negotiate plans to save jobs.
"There is nothing humiliating about negotiating plans to ensure jobs and communities are safe.
"This plant is on cold shut down and each day that goes by makes it harder to start back up again, which is why the stewards made the offer to the company so that we can get people back to work."
BOTH government ministers said they were hopeful the union agreement could produce a positive outcome.
Mr Swinney said: "The management were open with us about the details of the conversation they've had with the trade union, and the trade union were equally clear with me that there has been a complete acceptance by the trade union of the management survival plan.
"Clearly we're in a very different set of circumstances from before, given the announcement that's been made by Unite to accept the company's survival plan.
"I think that creates a much better basis for further progress towards resolving issues, and both the Scottish and the Westminster governments stand ready to do whatever we can to help
"I am hopeful that parties can reach an agreement which will lead to the reopening of the petrochemicals plant and retaining this important contribution to the Scottish economy."
Mr Carmichael said he was hopeful, but the decision rested purely with the Ineos shareholders.
He said: "It's clear that we're dealing with a different situation today following the statement from Unite that they were prepared to accept the Ineos survival plan without any pre-conditions.
"I think it's fair to say that we are in a much better place today in relation to the future of the plan than we were yesterday. There remains of course a great deal to be done."
"I think you have to be careful before you start getting too carried away. There's still a great deal of ground to be covered.
"What I detect as a result of the changed union position is a willingness to start covering that ground."
A spokeswoman for Ineos would only say there would be a statement released today.