Sir William McAlpine, who bought the steam locomotive for £25,000 in 1973, died in March.
Ticket sales for the trip on January 11 will fund a one-year engineering traineeship for a young person to learn how to maintain the engine.
The journey from London King’s Cross to York will be Flying Scotsman’s first run of the new year.
DB Cargo, Network Rail and LNER will also permanently rename a Class 90 electric locomotive in memory of Sir William, a director of the construction company Sir Robert McAlpine.
He saved Flying Scotsman when it was being stored at an army base in California after then owner Alan Pegler lost his fortune by touring it in the US.
Amid fears the locomotive would never return to the UK, Sir William negotiated a rescue deal and it was brought back across the Atlantic. He then paid for it to be restored and resume main line operations.
Jim Lowe, head of operations at current owner the National Railway Museum in York, paid tribute to Sir William for his “significant contribution to the museum and to the wider preservation of railway heritage in this country”.
He said: “Holding this memorial tour, naming a locomotive after him and, especially, setting up an engineering bursary to benefit young people, will create a fitting legacy to honour his memory.” Tickets for the memorial trip cost £159 in standard class and are available from UK Railtours.
The 95-year-old locomotive, reputedly the most famous in the world, was designed by Edinburgh-born Sir Nigel Gresley to haul the same-named Edinburgh-London express on the east coast main line.
It was the first steam locomotive to reach 100mph, in 1934, and set a record for the longest non-stop run, of 422 miles in Australia in 1989.
The engine was restored at a cost of more than £4 million by the National Railway Museum.
Earlier this month, trainspotters desperate to see the Flying Scotsman on tour were warned to take care.
Keen to get the perfect photo of the world’s most famous steam locomotive on one of the world’s most iconic stretches of railway line, there were fears that people may put themselves at risk.
Around the country police and rail bosses issued urgent warnings to train buffs over fears that someone could be killed.
Chief Inspector John Justice, from the British Transport Police, said during an earlier tour in Surrey: “So far on the Flying Scotsman tour there has been some disruption, with various incidents of trespass along the line.
“It is incredibly disappointing that despite repeated warnings, people chose to risk their lives and the lives of others by going onto the railway tracks to view the Flying Scotsman.”