Train services will be back to their usual Bank Holiday levels after a planned strike which would have caused widespread travel chaos was called off.
Unions suspended a 24-hour walkout due to start at 5pm on Monday after Network Rail tabled a new pay offer.
Leaders of the Rail, Maritime and Transport union (RMT) and Transport Salaried Staffs Association (TSSA) will now consult with members over the new offer, made after the rejection of a proposed four-year pay deal.
Rail companies had started cancelling services next week and warned passengers not to travel, but they quickly reversed their advice after the breakthrough.
However, a large amount of engineering work has been planned for the holiday weekend which will have an impact on certain routes.
Virgin West Coast, which had announced widespread cancellations, said its original timetable had been reinstated for Monday and Tuesday.
Other train operators said they would be running planned services.
RMT general secretary Mick Cash said: "Following the Acas talks, RMT has received a revised offer that enables us to suspend the planned industrial action while we consult in full with our Network Rail representatives."
Manuel Cortes, general secretary of the TSSA, said: "Our negotiating team at Acas has received a revised offer from Network Rail.
"As a result of this, they have suspended the planned industrial action, pending the outcome of a meeting of our workplace representatives next week."
Lawyers for Network Rail halted plans to take legal action against the TSSA in the light of developments.
Transport Secretary Patrick McLoughlin said: "I am very pleased that the unions have made a decision to suspend their planned action.
"Passengers right across the country will welcome this news and the knowledge that the extensive disruption threatening the Bank Holiday and the return to work on Tuesday has been averted.
"The Government has been working closely with transport operators, Highways England and local government on preparations to help manage the impact a national rail strike would have had on the network. We all welcome this news."
Anthony Smith, chief executive of the watchdog Transport Focus, said: "Passengers will be relieved that the planned industrial action has been called off. It is passengers who suffer most in the event of strikes.
"Many had already been inconvenienced and had to seek advice about their plans for the weekend. This reinforces what we have long said about the need for accurate, reliable, timely information."
Highways England had decided to extend the lifting of roadworks because rail travellers were expected to switch to the roads.
The organisation said it was reviewing the arrangements it had previously announced.