The trains will line up on the East Coast Main Line at Tollerton, North Yorkshire, at around 6am on Sunday before moving south to York.
Flying Scotsman will be joined by an HST and InterCity 225 from Virgin Trains' current fleet, as well as one of the operator's new Azuma trains, which come into service next year.
Those hoping to catch a glimpse of the trains are being urged to remain behind safety boundaries.
Taxpayer-funded Network Rail was forced to pay out almost £60,000 in compensation when 59 train services were delayed by people encroaching on the track to get as close as possible to Flying Scotsman during its inaugural run following a decade-long refit in February last year.
A giant screen at York station will broadcast live footage of the event.
Rob McIntosh, a managing director for Network Rail, which is responsible for managing Britain's railway infrastructure, said it would be a "prestigious and unique event for the people of Yorkshire".
He went on: "The area has a very proud rail heritage and by working closely with our industry partners we've been able to turn what has been a logistically challenging vision - to create an iconic railway moment on the East Coast Main Line without impacting on regular passengers - into what will be a truly special occasion."
The event will take place when no regular services use that section of the line.
David Horne, managing director for Virgin Trains on the East Coast, said: "We're delighted to present this unique event that showcases the past, present and future of rail travel in the UK, with Azuma travelling alongside Flying Scotsman and trains from our revamped current fleet.
"With our new Azuma trains entering service next year, this is an opportunity to celebrate the icons of the railways and look forward to 2018, when we'll usher in a new era for travel on the East Coast route."
Built in Doncaster, in 1923, Flying Scotsman soon became the star locomotive of the British railway system, pulling the first train to break the 100mph barrier in 1934.
Paul Kirkman, director of York's National Railway Museum, which owns the locomotive, said: "The East Coast Main Line has long been famed for speed and style.
"In the 19th century elegant locomotives were designed to haul trains on this route, cementing its reputation as a railway racing stretch operated by thoroughbred engines.
"The four-train line-up epitomises the evolution of the later generation of fast, elegant and stylish trains - all with a shared bloodline - that epitomise the history of the route from the 1850s to today."