The National Union of Rail, Maritime and Transport Workers (RMT) said 24-hour walkouts planned for this Saturday and Christmas Eve had been suspended following "significant progress" in talks with the train operator.
It also called off a separate 24-hour strike planned for Friday on CrossCountry trains, which operate between Scotland and England, following progress during talks with the company.
The RMT declined to discuss details of an offer tabled by ScotRail on Tuesday but the operator confirmed this does not include the union's key demand that ticket collector Scott Lewis be reinstated.
He was sacked for gross misconduct following a lengthy argument with passenger Luke Addis, 24, over a free ticket offer in March.
ScotRail claimed CCTV evidence showed Mr Lewis had been "intimidating and aggressive" and had reduced the passenger to tears. The allegations were described as a travesty by the RMT which claimed the ticket collector had been following company procedures for dealing with a fare dodger.
Industry sources said the latest round of talks this week had taken place amid a revolt by RMT members who faced losing pay as a result of the dispute.
The strike was called despite the action being backed by only 24% of those eligible to take part in the ballot.
A source said scores of staff had threatened to quit the union if the strike went ahead, claiming they were unhappy at "misleading" union claims that suggested no CCTV recording of the argument existed.
The RMT declined to comment on the allegations and said details of the settlement were confidential. However, a letter posted on the union's website by Bob Crow, its general secretary, said progress had been made in talks with ScotRail.
"Further to my letter dated December 13, 2012, I am happy to report that significant progress has been made in talks with ScotRail," Mr Crow wrote.
"I can confirm that a satisfactory agreement has now been reached between the union and the company.
"Having considered this matter, the union's executive has decided to suspend the industrial action."
The result was welcomed yesterday by ScotRail, whose spokesman said: "We are delighted common sense has prevailed and the threat of industrial action has been lifted.
"It is the right decision. Our customers can look forward to normal services over Christmas and can travel to be with family and friends."
The spokesman similarly declined to comment on the deal reached with the RMT, also describing it as confidential.
Transport Minister Keith Brown welcomed the announcement. He said: "It is a great relief to hear the RMT union and ScotRail have come to an agreement which sees the cancellation of the strikes planned by the union in the run-up to Christmas.
"I have spoken to both parties a number of times in the past few days, and at all times have encouraged them to keep talking and try to resolve these issues and ensure there is no disruption for passengers."
The RMT planned a series of national rail strikes in Scotland in 2010 in a row over who opens and shuts doors on a new train service operating on the Airdrie-Bathgate route.
As reported by the Sunday Herald at the time, the dispute was called off after a letter signed by 40 RMT members in Glasgow accused the union's executive of staging "an exercise in political grandstanding" which had not produced any effect.