Scottish transport minister Humza Yousaf gave more information on the £3 million set aside for fare offers announced in the Holyrood budget on Thursday.
As well as the free week for season-ticket holders, further offers for weekly ticket holders and daily commuters are also being worked on, and will be announced in the new year.
Mr Yousaf said: “We recognise any level of delay or disruption on the rail network in Scotland affects people’s lives.
“This year has been particularly challenging as we take forward our record-breaking investment programme on the live network to deliver newer, longer, greener trains on our flagship routes between Edinburgh and Glasgow as well as further afield.
“While we continue to monitor ScotRail’s delivery of their performance improvement plan, we are confident they can and will deliver the service we expect.
“Passengers rightly deserve an efficient and value-for-money rail network.
“That is why we have considered a number of options for rewarding passengers for their custom.
“During 2017, we will fund an initiative that gives one week’s travel free to monthly and annual ScotRail season ticket holders
“By offering a ‘free week’ we can in many instances match or even provide better savings for passengers than if we offered a fares freeze.
“As service improvements and investment also impact on those across the country who do not use season tickets, we will put in place a number of promotions and fare offers throughout the year to ensure they also benefit from this investment.”
Labour called for a fare freeze, claiming it would cost £2 million, but Finance Secretary Derek Mackay said the impact of a one-year fare freeze would cost £58 million by the time of the first break clause in the train operating franchise.
ScotRail Alliance managing director Phil Verster said: “The free week of travel for our season-ticket holders is a ‘thank you for your patience’ while we work to deliver a rail network that all of Scotland can be proud of.”
More details will be announced in the new year and ScotRail will set a specific period in 2017 when the free week will be available.
ScotRail has faced heavy criticism for late and cancelled trains, with campaigners calling for Dutch parent firm Abellio to be stripped of the franchise to run Scotland’s railways.