ScotRail said fares for four out of ten journeys would not increase while peak-time increases would be limited to inflation.
The annual fares increase is calculated using the July Retail Prices Index (RPI) rate of 2.5%.
Fares in England and Wales are calculated by RPI plus 1%, meaning an average increase of 3.5% for customers there.
Companies south of the border are also able to raise some fares by 2% above RPI.
Transport minister Keith Brown said the average rise in Scottish rail fares would be 1.9% as a result of a cap negotiated by the Scottish Government.
He said: "I have negotiated an agreement with ScotRail which means their peak fares will only increase by 2.5%, rather than up to 5.5% in England and Wales.
"The next ScotRail franchise will bear down further on the cost of fares, ensuring they will not rise above inflation, and it will be a condition of the next franchise that regulated off-peak fares will be restricted to 1% below inflation from 2016.
"From January 2016 regulated ScotRail fare increases can be no higher than RPI and off-peak regulated fare increases will be capped at 1% below RPI."