After a successful trial in West yorkshire, the scheme is being brought in on the Scarborough to Hull and Whitby to Middlesborough lines next month.
The company says penalty fares are designed to discourage people from travelling on trains without first paying for their tickets and passengers who do so could be fined £20 or double the cost of a single fare - whichever is the most.
Strike to affect trains from Bridlington and Scarborough this weekend.A statement by Northern said: "Penalty fares have been in place across the UK rail network for many years, and were introduced to Northern’s routes earlier this year with a trial in West Yorkshire. That trial was well received by customers and even some who were originally sceptical, praised the way in which it was been introduced and managed.
"Following the trial, penalty fares were rolled out more widely."
More lines, including those along the Yorkshire Coast, will adopt the scheme from Thursday, December 6.
Northern's statement added: "Most stations on penalty fare routes will have either ticket offices or ticket vending machines and so customers will have the opportunity to purchase tickets before they travel.
"In addition, tickets may be bought at any time before a customer boards a train by using the Northern App, with no booking fees incurred.
"If these facilities are not available at stations, or if offices are closed or machines out of order, customers will still be able to buy a ticket from the on-board conductor.
"Where customers want to pay cash, but ticket machines are card only, they will be able to obtain ‘promise to pay’ notices from the machines which can be presented, along with cash to the conductor – the full range of fares will still be available on board.
"If customers board from stations with ticket machines or staffed ticket offices, but do not have a valid ticket, they will only be eligible for standard fares if buying from the conductor. If a customer chooses to do this, they may be issued with a Penalty Fare if an authorised collector is encountered.
"We are investing millions of pounds to introduce more than 600 new ticket machines across the network and have developed our website and mobile app to give customers more options and to make buying a ticket easier than ever before.
"However, there will still be some circumstances in which customers are unable to buy tickets and our authorised collectors are able to use their discretion to ensure no-one faces unfair penalties.
"Where customers do feel a penalty fare has been applied wrongly there is a tried and tested, independent appeals process which is used across the country."