London North Eastern Railway (LNER) will replace off-peak return tickets for the routes with single tickets which cost nearly half the price.
For example, passengers travelling between London and Edinburgh who buy a ticket at the station are currently charged £146.40 for a single or £147.40 for a return.
The cost of a single would be slashed to £73.70 under the trial, which begins in January 2020.
Mr Shapps said the scheme would help create "a more convenient, flexible and fairly priced experience".
He continued: "This will save many people money with substantially cheaper single tickets, boost customer confidence, and ensure passengers up and down the country get the modern transport service they expect."
Jacqueline Starr, chief operating officer at industry body the Rail Delivery Group, said: "Passengers, businesses and rail companies are united in wanting easier fares.
"The trials on LNER's routes will help to support our proposed reforms and create a system that better fits how people live and work today.
"As the trial is being carried out, we want to work with Government to update current regulation to deliver the better fares system the public wants to see."
Campaign for Better Transport chief executive Darren Shirley said: "This trial is a welcome step towards fairer, simpler, more transparent ticketing.
"Single-leg pricing could make it easier for passengers to choose the most appropriate ticket for their journey and improve confidence that they are getting a good deal, but only if this is not used as a means to push up fares further."