Following what have been described as "informal discussions" over the past few months, the agreement was made for an initial two-year period.
Melmoe, who retired from Willerby Landscapes after 40 years in April 2017, after his company won BALI Awards Grand Award for a record sixth time, said there was "a natural synergy" between the way he and Bowles & Wyer chief executive John Wyer operates.
Wyer said the move was "a huge boost" for the company.
"We have always admired Willerby Landscapes, who built up an unrivalled reputation and sustained growth under John’s direction. We felt that there was a strong overlap between the two companies – we have a lot of shared values and both have developed business models built around long-term partnering with clients. We’re really excited to have John join us and look forward to learning a lot from his experience."
Melmoe is due to work with the design and build company on a number of internal projects, as well as attending board and strategy meetings.
He said: "As a result of mutual respect, it was an easy decision for me to join Bowles & Wyer to assist them in realising their long-term goals. These are indeed exciting times and I am very much looking forward to working with the staff to assist with the progression of the business."