East Coast, which operates between Scotland and London, said it had also frozen fares on 43 per cent of journeys.
Overall, fares will go up by an average of 2.8 per cent across Britain, with East Coast’s rise averaging 1.2 per cent, ScotRail’s 1.9 per cent and west coast cross-Border operator Virgin Trains’ 3.3 per cent.
The rail industry said it was the lowest rise for four years.
The RPI measure of inflation used to calculate fares is currently 2.6 per cent.
However, Labour, campaign groups and rail unions said fares were rising far faster than wages.
Transport minister Keith Brown said ScotRail’s peak fares would also be capped at in inflation in 2015, and off-peak fares would be frozen so long as inflation stayed below 3.5 per cent. The increase will add 70p to peak Edinburgh-Glasgow return tickets to £22.50. Off-peak return fares are £12.60.
Four in ten ScotRail passengers use off-peak tickets.
Mr Brown said: “Scotland’s railways are offering an ever more attractive travel option.
“The work being done between the Scottish Government and ScotRail to bear down on fares will draw even more people from the road on to the train.
“This will help us see a continuation of the shift from road to rail which has resulted 85 million passengers travelling on ScotRail services in the past year alone.”
Consumer group Which? said the fare increases “will be a blow to people already feeling the financial squeeze”.