It means ScotRail’s Anytime singles and returns, and Season Tickets, rise by 2.8 per cent.
Off-Peak singles and returns, which are generally available after 9am but not on some routes in the evening peak period, will increase by 1.8 per cent.
This compares to this year's rises of 3.2 per cent for peak fares and 2.2 per cent for off-peak.
ScotRail will announce later how much its unregulated fares will rise by - Super Off-peak, Advance and First Class tickets.
The cap on the annual rise in regulated fares, which cover about half of tickets sold, is linked to July's rate of Retail Prices Index (RPI) inflation, which was announced by the Office for National Statistics (ONS) as 2.8 per cent.
Off-peak fares on cross-Border operators such as LNER and CrossCountry will also increase by that amount.
Rail campaign groups warned that commuters will "refuse to pay" if season ticket prices continue to be hiked.
They have also called for the lower Consumer Prices Index (CPI) measure of inflation to be used to set fare increases, which are implemented from 2 January 2020.
The CPI rate increased to 2.1% last month, the ONS said.
A cap on how much they can be increased is pegged to the July RPI figure, except for off-peak fares on ScotRail, for which RPI -1 per cent is used.
Rail regulator the Office of Rail and Road said regulated fares went up by an average of 2.8 per cent in January, following the July 2018 RPI figure of 3.2 per cent.
A 2.8 per cent rise in season ticket prices would lead to an increase of more than £100 in the annual cost of getting to work for some commuters.
An annual season ticket between Edinburgh to Glasgow is expected to increase by £114 to £4,198.
A Scottish Government spokesperson said: “We are committed to ensuring that rail fares are affordable for passengers and taxpayers across Scotland.
"We have capped increases where we have influence, making fares 20 per cent cheaper on average than in the rest of Great Britain.
“While any fare increase is unwelcome, calls for measures such fares cuts or a fares freeze underestimate the impact of these on the public purse.
"Two-thirds of the cost of running the railway is already met through Scottish Government subsidy, with the remainder through rail passenger revenues.
"Any change to rail fares could therefore have a significant impact on the taxpayer.
“The ongoing UK-wide Williams review offers an opportunity to reform the broken rail franchise system.
"Rather than implement any measures prematurely, we await the UK Government’s white paper in the autumn before making fundamental change.
"This includes fares policy as we would need to understand how it would work within the context of any change to franchising.”
UK Transport Secretary Grant Shapps said he was "not delighted" about increasing rail fares.
He told BBC Radio 4's Today programme: "I'm not delighted by it, to be perfectly honest, as a train commuter.
"The truth is we do now have a situation where average wages are going up faster than inflation, so if you don't keep this tracking with inflation you are actually effectively putting less money into transport and less money into trains and you won't get them running on time doing that either."
Shadow transport secretary Andy McDonald said: "Every year commuters are being asked to pay more money for bad train services.
"The Government has sat back and allowed private train companies to cash in while people's pay has been held back. Continuous fare rises undermine urgent action to tackle the climate emergency by pricing people off the railways.
"Labour will bring our railways into public ownership so they are run in the interests of passengers, not private profit."
Research by passenger watchdog Transport Focus shows that fewer than a third of rail commuters are satisfied with the value for money of their ticket.
Director David Sidebottom said: "We believe it's time for a fairer, clearer fares formula based on calculations that use the Consumer Prices Index, rather than the discredited Retail Price Index.
"After recent disruption and a lot of misery over last winter, rail operators still have a great deal to improve."
Bruce Williamson, spokesman for campaign group Railfuture, said: "It might be that we've now reached the point where we cannot simply put fares up and expect passengers to take the hit.
"They will just give up and refuse to pay.
"They will either find either another job or another form of transport."