The rise is lower than a previously planned 4.1% and follows moves in England to raise in line with inflation.
The decision to cap regulated fare increases at Retail Price Index, instead of RPI+1%, comes months after the Scottish Government promised the same for people using Scotrail services. Regulated fares include season tickets, single and off-peak journeys.
The rises mean a return fare from Glasgow or Edinburgh to London will be about £1 cheaper than it would have been with RPI+1%.
The UK Government sets fare increases for rail services in England and cross-Border services while the Scottish and Welsh governments set tariffs for their domestic services.