Mostyn-Jones, who took up his new role this week, joins First Milk from Arla Foods UK where he was operations director.
He has also held senior roles with Express Dairies, Unigate and Heinz. A spokesman for First Milk said that it was a newly created role for the company to allow chief executive officer Peter Humphreys to focus on business development and acquisition plans.
Humphreys said: "This is a key time in the development of First Milk and we are very fortunate to have someone of Richard's ability. He has broad operational, account management and strategic experience which will assist us in taking the next steps in our journey to build a fully integrated dairy business.
"We have worked hard over the past 12 months to hone our business strategy and to bring individuals with a strong record of delivery into First Milk in order to complement our range of skills.
"Richard will now play a key role in overseeing our sales, distribution and membership functions."
Mostyn-Jones added: "First Milk is in an exciting phase of its development, with a sound strategy and ambitious plans. "
His appointment is the third change to the co-op's senior management recently. In November last year, Humphreys replaced John Duncan as chief executive officer, while in March this year Eric Sanderson replaced Andrew Young as a non-executive director.