The team from the Penrith-based company will complete a course winding across Cumbria over seven days from Monday 2 and Tuesday 10 July.
In total, 22 members of staff, half of the workforce, will take part in the challenge, which covers mountains and other rugged terrains around the county.
In addition to marking 140 years the challenge is also supporting Macmillan Cancer Support, in recognition of the help it provided for one of the company’s longest-serving employees, Malcolm Warwick, who passed away in 2006.
David Warwick, Malcolm’s son, who also works at the business, will take part in the final leg of the relay and be welcomed home by Malcolm's widow Pat and his sister Marjorie.
Managing director Andy Jackson, who will be cycling on the first day, said: “We hope to raise £1,400, which ties into the theme of 140. We wanted to engage with staff and customers in a positive way.
“We decided a relay around parts of Cumbria including some of the locations where the company has been based over the years would be both poignant and celebratory.”
Starting at the company’s Penrith office, the route heads up to Carlisle then through Borrowdale and Keswick, calling at H&H Reeds Printers in Milnthorpe.
Then the staff move on to Kendal and Ullswater before the final leg back to H&H Reeds Printers in Penrith. The relay begins with a 10-mile run followed by a mixture of cycling, and walking.
Donations can be made at: https://www.justgiving.com/fundraising/hhreeds140