The 70-year-old decided to move on with his contract up for renewal and owner Ann Budge stepping back from daily operations at the club.
Jefferies and Budge had worked closely since the former manager returned to Hearts as an advisor last summer.
He helped manager Robbie Neilson with player signings and also enjoyed a strong relationship with Budge behind the scenes.
With Budge ceding responsibility for day-to-day club business to chief executive Andrew McKinlay, Jefferies has chosen to step away from his consultancy position in what was an amicable parting.
Hearts will soon appoint a new head of recruitment following John Murray’s decision to retire, while sporting director Joe Savage is helping Neilson execute this summer’s recruitment plan.
The club’s competitive season starts this weekend with a visit to Peterhead in the Premier Sports Cup.