The Scottish government included funding for the scheme in its budget following criticism of rail services.
Fares will rise in 2017, but Transport Minister Humza Yousaf said passengers with monthly or annual season tickets will get a week's worth of free travel.
Scottish Labour, which has called for a freeze on all rail fares, said the plans do not go far enough.
They said the "vast majority" of passengers would still face record fares in January.
Finance Secretary Derek Mackay announced the plans during his budget statement, where he claimed a full freeze would be too expensive and would hit investment in the rail network.
The government said its plans could deliver greater savings for customers with annual or monthly season tickets even with fares set to rise in 2017, and said further deals would be announced for other passengers.
Mr Yousaf said he was confident ScotRail could deliver "the service we expect", after a "particularly challenging" year of delays and disruptions on the network.
He said: "Passengers rightly deserve an efficient and value for money rail network.
"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.
"And 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."
An example cited by the government was that the cost of annual and monthly season tickets between Glasgow and Edinburgh will go up by £72 and £82.80 in 2017 respectively, while they claim the 'free week' plan would see regular travellers save £95.50.
ScotRail will designate a specific period in 2017 during which the free travel will be available.
The group's managing director Phil Verster said the network was undergoing its biggest upgrade since Victorian times.
He said: "Our customers have been incredibly patient during the big projects like Winchburgh Tunnel last year and Queen Street Tunnel earlier this year.
"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."
However opposition parties said the measures do not go far enough.
Labour's transport spokesman Neil Bibby said the government had been "forced" into concessions by pressure from politicians and passengers - but said the plans didn't "hit the mark".
He said: "Labour's fare freeze policy would have benefited every ScotRail passenger - the SNP's policy won't.
"After all the delays and disruption people have had to put up with on the railways, no passenger should face a fare hike in the New Year.
"The bottom line is that fares will still rise to record levels in January for the vast majority of passengers as planned. It is insulting to ask passengers to pay a penny more for the shocking ScotRail service they have been receiving."

But there have been many such agreements in the past and the omens for peace in the region are not good.
Russian-backed fighters and the Ukrainian army have clashed almost daily for the last 30 months.
At the beginning of January there was a serious escalation in the violence.
Ukraine said two of its soldiers had been killed and 16 injured in fighting over the weekend.
In theory the two sides will this week pull back heavy weaponry from areas near the front line.
But a source at the Munich talks over the weekend told the BBC that no progress had been made in reaching a political solution.
A £3m package of "targeted discounts" for Scottish rail passengers with season tickets has been announced.
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A ceasefire is due to come into effect in eastern Ukraine following a deal in Munich over the weekend to halt fighting and withdraw heavy weapons from the front line.