They will now be presented to their respective organisations in the hope a walkout can be avoided.
The details of the proposals, which could yet be rejected, will remain confidential unless Unite or the oil companies themselves decide to go public.
Sky News understands that Unite will be presenting them to their representatives on Monday.
Assistant general secretary of Unite, Diana Holland, said: "We have done as much as we can and we have a document we can now discuss but we will keep the process confidential until the people who matter make the decision."
Peter Harwood, Acas chief conciliator, described the talks as "challenging" but said: "Acas is pleased at this development and hope that the matter will soon be settled."
Earlier on Friday, Unite was given an extension to the deadline for declaring industrial action so that negotiations could continue.
Under employment law, the union should have decided by late afternoon whether to call its 2,000 members in the industry out on strike after the vote last month.
The dispute has been brewing for more than a year but flared up in March when Unite announced that workers in five firms had voted to strike.
The union has been demanding minimum standards on pay, hours, holiday and redundancy as well as action on health and safety.
There was a spate of panic-buying of fuel by motorists last month after the Government advised them to top up their tanks because of the threat of a walkout.
Chaotic scenes and long queues were seen at garages across the country following the Government's advice, which was heavily criticised.
Following the agreement of the proposals, a spokesman for the Energy Department said: "The Government welcomes the news that Unite plan to put a deal to their members.
"We hope that this will lead to the threat of strike action being lifted. The Government continues to believe that any strike action is wrong and unnecessary.
"We will continue to work on contingency plans to increase the country's resilience in the event of a strike."