Dagley will continue to buy Majestic's fine wine and Bordeaux ranges.
He takes over from John Thorogood, who has left the business after 44 years, and will now concentrate on consultancy work.
Lay & Wheeler, acquired by Majestic in March, specialises in the sale of fine wines to customers who keep their purchases in storage under bond. It is operated separately from the main Majestic business.
Lay & Wheeler managing director Jeremy Palmer said: “Appointing Nick is an exciting development.
"Lay & Wheeler has relationships with top producers around the world, and he will work to maintain and grow them. At the same time he will bring the commercial knowledge and skills learnt at Majestic to the company.
"Using this partnership we aim to introduce many new customers to Lay & Wheeler.”