The route features the iconic Ribblehead Viaduct, which has 24 arches spanning a quarter of a mile (400m), 104ft (31.7m) above the ground.
The Settle Carlisle Railway Development Company will be running a chartered steam train between Carlisle and York on 25 May.
Northern will also offer £1.50 tickets to customers travelling on the route to mark the milestone.
About 6,000 workers contributed to its complex construction, which includes 14 tunnels and more than 20 viaducts along its 72 miles (116km) of track.
In 1983, British Rail announced plans to close the line to passengers amid concerns about the cost of repairing the Ribblehead Viaduct. However, the plan was scrapped after a successful public campaign.
The Settle Carlisle Railway Development Company’s chairman, Pete Myers, said the company was working with communities along the line to mark the “special anniversary year”.
He said: “The Settle to Carlisle line is unique, connecting communities from Yorkshire through to Cumbria, and also providing a sustainable and beautiful way for visitors to explore the Yorkshire Dales, Westmorland Dales and Lake District.”
